Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
3rd Edition
ISBN: 9780134766850
Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher: PEARSON
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Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
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Chapter 8.4, Problem 37E
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Use substitution to evaluate the definite integral (no decimal point)
Gaussian functions G.1 G.2 G.3 G.4 G.5 G.6 G.7 G.8 8 S 8 0 e-ax² 8 1 [["new" daw ! dx= 0 2a dx= 8 [x²e-dx-1(5) x²e-ax² dx = 4 1 T erfz= 8 S™ 0 11 S x³e-ax² dx= 0 0 2 a 2 3 [x²e-max->()" x¹e-ax² dx= 1 2q² So 1/2 1/2 e-x² dx 1/2 TC¹ m! x² ₂2m+1e¬ax² dx = 2qm+1 x²me-ax² dx = 1/2 erfc z=1-erf z (2m-1)!! T 2m+1 am (2m-1)!!=1×3×5...×(2m-1) (1) a 1/2
Evaluate the definite integral by using substitution. 6. X -1 dx -1 (x+2)2/3 4.

Chapter 8 Solutions

Calculus, Single Variable: Early Transcendentals (3rd Edition)

Ch. 8.1 - What change of variable would you use for the...Ch. 8.1 - Prob. 2QCCh. 8.1 - Prob. 3QCCh. 8.1 - Prob. 4QCCh. 8.1 - What change of variables would you use for the...Ch. 8.1 - Prob. 2ECh. 8.1 - What trigonometric identity is useful in...Ch. 8.1 - Prob. 4ECh. 8.1 - Prob. 5ECh. 8.1 - Prob. 6E
Ch. 8.1 - Substitution Review Evaluate the following...Ch. 8.1 - Prob. 8ECh. 8.1 - Substitution Review Evaluate the following...Ch. 8.1 - Prob. 10ECh. 8.1 - Substitution Review Evaluate the following...Ch. 8.1 - Prob. 12ECh. 8.1 - Substitution Review Evaluate the following...Ch. 8.1 - Integration review Evaluate the following...Ch. 8.1 - Subtle substitutions Evaluate the following...Ch. 8.1 - Integration review Evaluate the following...Ch. 8.1 - Integration review Evaluate the following...Ch. 8.1 - Prob. 18ECh. 8.1 - Integration review Evaluate the following...Ch. 8.1 - Prob. 20ECh. 8.1 - Integration review Evaluate the following...Ch. 8.1 - Prob. 22ECh. 8.1 - Prob. 23ECh. 8.1 - Prob. 24ECh. 8.1 - Integration review Evaluate the following...Ch. 8.1 - Prob. 26ECh. 8.1 - Splitting fractions Evaluate the following...Ch. 8.1 - Prob. 28ECh. 8.1 - Integration review Evaluate the following...Ch. 8.1 - Prob. 30ECh. 8.1 - Completing the square Evaluate the following...Ch. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - Prob. 35ECh. 8.1 - Prob. 36ECh. 8.1 - Completing the square Evaluate the following...Ch. 8.1 - Prob. 38ECh. 8.1 - Prob. 39ECh. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Integration reviewEvaluate the following integrals...Ch. 8.1 - Prob. 46ECh. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Integration reviewEvaluate the following...Ch. 8.1 - Prob. 50ECh. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.1 - Integration reviewEvaluate the following...Ch. 8.1 - Miscellaneous integrals Use the approaches...Ch. 8.1 - Miscellaneous integrals Use the approaches...Ch. 8.1 - Miscellaneous integrals Use the approaches...Ch. 8.1 - Prob. 57ECh. 8.1 - Prob. 58ECh. 8.1 - Prob. 59ECh. 8.1 - Prob. 60ECh. 8.1 - Miscellaneous integrals Use the approaches...Ch. 8.1 - Prob. 62ECh. 8.1 - Prob. 63ECh. 8.1 - Prob. 64ECh. 8.1 - Prob. 65ECh. 8.1 - Prob. 66ECh. 8.1 - Prob. 67ECh. 8.1 - Prob. 68ECh. 8.1 - Different substitutions a. Evaluate tanxsec2xdx...Ch. 8.1 - Prob. 70ECh. 8.1 - Different methods a. Evaluate x2x+1dx using the...Ch. 8.1 - Prob. 72ECh. 8.1 - Prob. 73ECh. 8.1 - Prob. 74ECh. 8.1 - Volume of a solidConsider the Region R bounded by...Ch. 8.1 - Prob. 76ECh. 8.1 - Surface area Let f(x)=x+1. Find the area of the...Ch. 8.1 - Prob. 78ECh. 8.1 - Prob. 79ECh. 8.1 - Prob. 80ECh. 8.2 - What are the best choices for u and dv in...Ch. 8.2 - Prob. 2QCCh. 8.2 - Prob. 3QCCh. 8.2 - Prob. 1ECh. 8.2 - Prob. 2ECh. 8.2 - Prob. 3ECh. 8.2 - Prob. 4ECh. 8.2 - Prob. 5ECh. 8.2 - How would you choose dv when evaluating xneaxdx...Ch. 8.2 - Prob. 7ECh. 8.2 - Prob. 8ECh. 8.2 - Integration by partsEvaluate the following...Ch. 8.2 - Integration by parts Evaluate the following...Ch. 8.2 - Prob. 11ECh. 8.2 - Prob. 12ECh. 8.2 - Integration by partsEvaluate the following...Ch. 8.2 - Prob. 14ECh. 8.2 - Integration by partsEvaluate the following...Ch. 8.2 - Prob. 16ECh. 8.2 - Prob. 17ECh. 8.2 - Prob. 18ECh. 8.2 - Integration by parts Evaluate the following...Ch. 8.2 - Integration by parts Evaluate the following...Ch. 8.2 - Integration by parts Evaluate the following...Ch. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Repeated integration by parts Evaluate the...Ch. 8.2 - Repeated integration by parts Evaluate the...Ch. 8.2 - Prob. 26ECh. 8.2 - Integration by partsEvaluate the following...Ch. 8.2 - Repeated integration by parts Evaluate the...Ch. 8.2 - Prob. 29ECh. 8.2 - Repeated integration by parts Evaluate the...Ch. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Definite integrals Evaluate the following definite...Ch. 8.2 - Definite integrals Evaluate the following definite...Ch. 8.2 - Definite integrals Evaluate the following definite...Ch. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Integration by partsEvaluate the following...Ch. 8.2 - Prob. 40ECh. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Volumes of solids Find the volume of the solid...Ch. 8.2 - Volumes of solidsFind the volume of the solid that...Ch. 8.2 - Volumes of solids Find the volume of the solid...Ch. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - Prob. 50ECh. 8.2 - Reduction formulas Use integration by parts to...Ch. 8.2 - Prob. 52ECh. 8.2 - Prob. 53ECh. 8.2 - Applying reduction formulas Use the reduction...Ch. 8.2 - Prob. 55ECh. 8.2 - Prob. 56ECh. 8.2 - Prob. 57ECh. 8.2 - Two methods Evaluate 0/3sinxln(cosx)dx in the...Ch. 8.2 - Two methods a. Evaluate xx+1dx using integration...Ch. 8.2 - Prob. 60ECh. 8.2 - Logarithm base b Prove that logbxdx=1lnb(xlnxx)+C.Ch. 8.2 - Prob. 62ECh. 8.2 - Combining two integration methods Evaluate cosxdx...Ch. 8.2 - Prob. 64ECh. 8.2 - Prob. 65ECh. 8.2 - Prob. 66ECh. 8.2 - Prob. 67ECh. 8.2 - Log integrals Use integration by parts to show...Ch. 8.2 - Comparing volumes Let R be the region bounded by y...Ch. 8.2 - Prob. 70ECh. 8.2 - Solid of revolution Find the volume of the solid...Ch. 8.2 - Between the sine and inverse sine Find the area of...Ch. 8.2 - Prob. 73ECh. 8.2 - Integrating inverse functions Assume that f has an...Ch. 8.2 - Oscillator displacements Suppose a mass on a...Ch. 8.2 - Prob. 76ECh. 8.2 - Prob. 77ECh. 8.2 - Practice with tabular integration Evaluate the...Ch. 8.2 - Prob. 79ECh. 8.2 - Prob. 80ECh. 8.2 - Prob. 81ECh. 8.2 - A family of exponentials The curves y = xeax are...Ch. 8.3 - Evaluate sin3xdxby splitting off a factor of sin x...Ch. 8.3 - Prob. 2QCCh. 8.3 - State the half-angle identities used to integrate...Ch. 8.3 - State the three Pythagorean identities.Ch. 8.3 - Prob. 3ECh. 8.3 - Prob. 4ECh. 8.3 - Prob. 5ECh. 8.3 - Prob. 6ECh. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - Integrals of sin x or cos x Evaluate the following...Ch. 8.3 - Prob. 10ECh. 8.3 - Trigonometric integralsEvaluate the following...Ch. 8.3 - Prob. 12ECh. 8.3 - Integrals of sin x or cos x Evaluate the following...Ch. 8.3 - Integrals of sin x or cos x Evaluate the following...Ch. 8.3 - Integrals of sin x and cos x Evaluate the...Ch. 8.3 - Prob. 16ECh. 8.3 - Integrals of sin x and cos x Evaluate the...Ch. 8.3 - Prob. 18ECh. 8.3 - Trigonometric integrals Evaluate the following...Ch. 8.3 - Prob. 20ECh. 8.3 - Trigonometric integrals Evaluate the following...Ch. 8.3 - Prob. 22ECh. 8.3 - Integrals of sin x and cos x Evaluate the...Ch. 8.3 - Prob. 24ECh. 8.3 - Integrals of sin x and cos x Evaluate the...Ch. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - Integrals of tan x or cot x Evaluate the following...Ch. 8.3 - Integrals of tan x or cot x Evaluate the following...Ch. 8.3 - Integrals of tan x or cot x Evaluate the following...Ch. 8.3 - Integrals of tan x or cot x Evaluate the following...Ch. 8.3 - Prob. 32ECh. 8.3 - Prob. 33ECh. 8.3 - Prob. 34ECh. 8.3 - Integrals involving tan x and sec x Evaluate the...Ch. 8.3 - Prob. 36ECh. 8.3 - Additional integrals Evaluate the following...Ch. 8.3 - Integrals involving tan x and sec x Evaluate the...Ch. 8.3 - Additional integrals Evaluate the following...Ch. 8.3 - Prob. 40ECh. 8.3 - Prob. 41ECh. 8.3 - Integrals involving tan x and sec x Evaluate the...Ch. 8.3 - Prob. 43ECh. 8.3 - Prob. 44ECh. 8.3 - Integrals involving tan x and sec x Evaluate the...Ch. 8.3 - Prob. 46ECh. 8.3 - Integrals involving tan x and sec x Evaluate the...Ch. 8.3 - Integrals involving tan x and sec x Evaluate the...Ch. 8.3 - Prob. 49ECh. 8.3 - Prob. 50ECh. 8.3 - Prob. 51ECh. 8.3 - Trigonometric integrals Evaluate the following...Ch. 8.3 - Integrals involving tan x and sec x Evaluate the...Ch. 8.3 - Additional integrals Evaluate the following...Ch. 8.3 - Integrals involving tan x and sec x Evaluate the...Ch. 8.3 - Prob. 56ECh. 8.3 - Additional integrals Evaluate the following...Ch. 8.3 - Prob. 58ECh. 8.3 - Square roots Evaluate the following integrals. 59....Ch. 8.3 - Prob. 60ECh. 8.3 - Square roots Evaluate the following integrals. 61....Ch. 8.3 - Arc length Find the length of the curve y = ln...Ch. 8.3 - Explain why or why not Determine whether the...Ch. 8.3 - Prob. 64ECh. 8.3 - Prob. 65ECh. 8.3 - Prob. 66ECh. 8.3 - Integrals of the form sinmxcosnxdx Use the...Ch. 8.3 - Prob. 68ECh. 8.3 - Prob. 69ECh. 8.3 - Prob. 70ECh. 8.3 - Prob. 71ECh. 8.3 - Prob. 72ECh. 8.3 - Prob. 73ECh. 8.3 - Prob. 74ECh. 8.3 - Prob. 75ECh. 8.4 - Use a substitution of the form x = a sin to...Ch. 8.4 - Prob. 2QCCh. 8.4 - Prob. 3QCCh. 8.4 - What change of variables is suggested by an...Ch. 8.4 - What change of variables is suggested by an...Ch. 8.4 - What change of variables is suggested by an...Ch. 8.4 - If x = 4 tan , express sin in terms of x.Ch. 8.4 - If x = 2 sin , express cot in terms of x.Ch. 8.4 - If x = 8 sec , express tan in terms of x.Ch. 8.4 - Sine substitution Evaluate the following...Ch. 8.4 - Prob. 8ECh. 8.4 - Sine substitution Evaluate the following...Ch. 8.4 - Sine substitution Evaluate the following...Ch. 8.4 - Sine substitution Evaluate the following...Ch. 8.4 - Sine substitution Evaluate the following...Ch. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Prob. 15ECh. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Prob. 18ECh. 8.4 - Prob. 19ECh. 8.4 - Prob. 20ECh. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Prob. 22ECh. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Prob. 24ECh. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Prob. 26ECh. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Prob. 28ECh. 8.4 - Prob. 29ECh. 8.4 - Prob. 30ECh. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Prob. 34ECh. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Prob. 36ECh. 8.4 - Prob. 37ECh. 8.4 - Prob. 38ECh. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Prob. 40ECh. 8.4 - Prob. 41ECh. 8.4 - Prob. 42ECh. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Prob. 44ECh. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Prob. 46ECh. 8.4 - Prob. 47ECh. 8.4 - Prob. 48ECh. 8.4 - Prob. 49ECh. 8.4 - Prob. 50ECh. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Trigonometric substitutions Evaluate the following...Ch. 8.4 - Prob. 55ECh. 8.4 - Prob. 56ECh. 8.4 - Prob. 57ECh. 8.4 - Prob. 58ECh. 8.4 - Area of a segment of a circle Use two approaches...Ch. 8.4 - Completing the square Evaluate the following...Ch. 8.4 - Completing the squareEvaluate the following...Ch. 8.4 - Prob. 62ECh. 8.4 - Completing the square Evaluate the following...Ch. 8.4 - Prob. 64ECh. 8.4 - Prob. 65ECh. 8.4 - Prob. 66ECh. 8.4 - Prob. 67ECh. 8.4 - Prob. 68ECh. 8.4 - Prob. 69ECh. 8.4 - Prob. 70ECh. 8.4 - Prob. 71ECh. 8.4 - Prob. 72ECh. 8.4 - Prob. 73ECh. 8.4 - Prob. 74ECh. 8.4 - Prob. 75ECh. 8.4 - Prob. 76ECh. 8.4 - Prob. 77ECh. 8.4 - Prob. 78ECh. 8.4 - Prob. 79ECh. 8.4 - Prob. 80ECh. 8.4 - Prob. 81ECh. 8.4 - Prob. 82ECh. 8.4 - Prob. 83ECh. 8.4 - Prob. 85ECh. 8.4 - Prob. 86ECh. 8.5 - Find an antiderivative of f(x)=1x2+2x+4.Ch. 8.5 - Prob. 2QCCh. 8.5 - Prob. 3QCCh. 8.5 - Prob. 4QCCh. 8.5 - Prob. 1ECh. 8.5 - Give an example of each of the following. a. A...Ch. 8.5 - What term(s) should appear in the partial fraction...Ch. 8.5 - What is the first step in integrating x2+2x3x+1?Ch. 8.5 - Set up the appropriate form of the partial...Ch. 8.5 - Prob. 6ECh. 8.5 - Prob. 7ECh. 8.5 - Prob. 8ECh. 8.5 - Set up the appropriate form of the partial...Ch. 8.5 - Prob. 10ECh. 8.5 - Prob. 11ECh. 8.5 - Prob. 12ECh. 8.5 - Set up the appropriate form of the partial...Ch. 8.5 - Set up the appropriate form of the partial...Ch. 8.5 - Prob. 15ECh. 8.5 - Prob. 16ECh. 8.5 - Setting up partial fraction decomposition Give the...Ch. 8.5 - Prob. 18ECh. 8.5 - Prob. 19ECh. 8.5 - Prob. 20ECh. 8.5 - Give the partial fraction decomposition for the...Ch. 8.5 - Prob. 22ECh. 8.5 - IntegrationEvaluate the following integrals....Ch. 8.5 - Prob. 24ECh. 8.5 - IntegrationEvaluate the following integrals. 25....Ch. 8.5 - Simple linear factors Evaluate the following...Ch. 8.5 - IntegrationEvaluate the following integrals. 27....Ch. 8.5 - Prob. 28ECh. 8.5 - Prob. 29ECh. 8.5 - IntegrationEvaluate the following integrals. 30....Ch. 8.5 - Prob. 31ECh. 8.5 - Integration Evaluate the following integrals. 32....Ch. 8.5 - Integration Evaluate the following integrals. 33....Ch. 8.5 - Prob. 34ECh. 8.5 - Simple linear factors Evaluate the following...Ch. 8.5 - Prob. 36ECh. 8.5 - Simple linear factors Evaluate the following...Ch. 8.5 - Prob. 38ECh. 8.5 - Repeated linear factors Evaluate the following...Ch. 8.5 - Prob. 40ECh. 8.5 - Repeated linear factors Evaluate the following...Ch. 8.5 - Prob. 42ECh. 8.5 - Repeated linear factors Evaluate the following...Ch. 8.5 - Repeated linear factors Evaluate the following...Ch. 8.5 - Repeated linear factors Evaluate the following...Ch. 8.5 - Prob. 46ECh. 8.5 - Integration Evaluate the following integrals. 47....Ch. 8.5 - Prob. 48ECh. 8.5 - Prob. 49ECh. 8.5 - Integration Evaluate the following integrals. 50....Ch. 8.5 - Integration Evaluate the following integrals. 51....Ch. 8.5 - Prob. 52ECh. 8.5 - Prob. 53ECh. 8.5 - Prob. 54ECh. 8.5 - Integration Evaluate the following integrals. 55....Ch. 8.5 - Prob. 56ECh. 8.5 - Prob. 57ECh. 8.5 - Prob. 58ECh. 8.5 - Integration Evaluate the following integrals. 59....Ch. 8.5 - Prob. 60ECh. 8.5 - Prob. 61ECh. 8.5 - Prob. 62ECh. 8.5 - Prob. 63ECh. 8.5 - Prob. 64ECh. 8.5 - Prob. 65ECh. 8.5 - Prob. 66ECh. 8.5 - Areas of regions Find the area of the following...Ch. 8.5 - Prob. 68ECh. 8.5 - Prob. 69ECh. 8.5 - Prob. 70ECh. 8.5 - Volumes of solids Find the volume of the following...Ch. 8.5 - Prob. 72ECh. 8.5 - Prob. 73ECh. 8.5 - Prob. 76ECh. 8.5 - Prob. 77ECh. 8.5 - Prob. 78ECh. 8.5 - Prob. 79ECh. 8.5 - Prob. 80ECh. 8.5 - Prob. 81ECh. 8.5 - Prob. 82ECh. 8.5 - Prob. 83ECh. 8.5 - Prob. 84ECh. 8.5 - Prob. 85ECh. 8.5 - Prob. 86ECh. 8.5 - Prob. 87ECh. 8.5 - Prob. 88ECh. 8.5 - Prob. 89ECh. 8.5 - Prob. 90ECh. 8.5 - Prob. 91ECh. 8.5 - Prob. 92ECh. 8.5 - Prob. 93ECh. 8.5 - Prob. 94ECh. 8.5 - Prob. 95ECh. 8.5 - Prob. 96ECh. 8.6 - Use Table 8.1 (p. 520) to complete the process of...Ch. 8.6 - Prob. 2QCCh. 8.6 - Prob. 3QCCh. 8.6 - Prob. 1ECh. 8.6 - Prob. 2ECh. 8.6 - Prob. 3ECh. 8.6 - Prob. 4ECh. 8.6 - Prob. 5ECh. 8.6 - Prob. 6ECh. 8.6 - Evaluate the following integrals. 7. 0/2sin1+cosdCh. 8.6 - Prob. 8ECh. 8.6 - Evaluate the following integrals. 9. 46dx8xx2Ch. 8.6 - Prob. 10ECh. 8.6 - Prob. 11ECh. 8.6 - Prob. 12ECh. 8.6 - Prob. 13ECh. 8.6 - Prob. 14ECh. 8.6 - Evaluate the following integrals. 15. 142xxdxCh. 8.6 - Evaluate the following integrals. 16. dxx41Ch. 8.6 - Prob. 17ECh. 8.6 - Prob. 18ECh. 8.6 - Prob. 19ECh. 8.6 - Prob. 20ECh. 8.6 - Evaluate the following integrals. 21. x9ln3xdxCh. 8.6 - Prob. 22ECh. 8.6 - Evaluate the following integrals. 23....Ch. 8.6 - Prob. 24ECh. 8.6 - Evaluate the following integrals. 25. dxx1x2Ch. 8.6 - Evaluate the following integrals. 26....Ch. 8.6 - Prob. 27ECh. 8.6 - Prob. 28ECh. 8.6 - Evaluate the following integrals. 29....Ch. 8.6 - Prob. 30ECh. 8.6 - Evaluate the following integrals. 31. 369x2dxCh. 8.6 - Prob. 32ECh. 8.6 - Prob. 33ECh. 8.6 - Prob. 34ECh. 8.6 - Evaluate the following integrals. 35....Ch. 8.6 - Prob. 36ECh. 8.6 - Prob. 37ECh. 8.6 - Prob. 38ECh. 8.6 - Prob. 39ECh. 8.6 - Prob. 40ECh. 8.6 - Prob. 41ECh. 8.6 - Prob. 42ECh. 8.6 - Evaluate the following integrals. 43. x91x20dxCh. 8.6 - Prob. 44ECh. 8.6 - Prob. 45ECh. 8.6 - Prob. 46ECh. 8.6 - Prob. 47ECh. 8.6 - Prob. 48ECh. 8.6 - Prob. 49ECh. 8.6 - Prob. 50ECh. 8.6 - Evaluate the following integrals. 51....Ch. 8.6 - Prob. 52ECh. 8.6 - Prob. 53ECh. 8.6 - Prob. 54ECh. 8.6 - Evaluate the following integrals. 55....Ch. 8.6 - Prob. 56ECh. 8.6 - Evaluate the following integrals. 57. sinxdxCh. 8.6 - Evaluate the following integrals. 58. w2tan1wdwCh. 8.6 - Prob. 59ECh. 8.6 - Prob. 60ECh. 8.6 - Prob. 61ECh. 8.6 - Prob. 62ECh. 8.6 - Prob. 63ECh. 8.6 - Prob. 64ECh. 8.6 - Evaluate the following integrals. 65. 01/6dx19x2Ch. 8.6 - Prob. 66ECh. 8.6 - Evaluate the following integrals. 67. x219x2dxCh. 8.6 - Prob. 68ECh. 8.6 - Prob. 69ECh. 8.6 - Prob. 70ECh. 8.6 - Prob. 71ECh. 8.6 - Evaluate the following integrals. 72. x2sinhxdxCh. 8.6 - Prob. 73ECh. 8.6 - Evaluate the following integrals. 74. e3xex1dxCh. 8.6 - Prob. 75ECh. 8.6 - Evaluate the following integrals. 76. xx2+6x+18dxCh. 8.6 - Evaluate the following integrals. 77. cos1xdxCh. 8.6 - Prob. 78ECh. 8.6 - Prob. 79ECh. 8.6 - Prob. 80ECh. 8.6 - Prob. 81ECh. 8.6 - Prob. 82ECh. 8.6 - Evaluate the following integrals. 83....Ch. 8.6 - Prob. 84ECh. 8.6 - Prob. 85ECh. 8.6 - Prob. 86ECh. 8.6 - Prob. 87ECh. 8.6 - Prob. 88ECh. 8.6 - Prob. 89ECh. 8.6 - Prob. 90ECh. 8.6 - Prob. 91ECh. 8.6 - Prob. 92ECh. 8.6 - Evaluate the following integrals. 93....Ch. 8.6 - Prob. 94ECh. 8.6 - Prob. 95ECh. 8.6 - Prob. 96ECh. 8.6 - Prob. 97ECh. 8.6 - Prob. 98ECh. 8.6 - Surface area Find the area of the surface...Ch. 8.7 - Use the result of Example 3 to evaluate...Ch. 8.7 - Prob. 2QCCh. 8.7 - Prob. 3QCCh. 8.7 - Prob. 1ECh. 8.7 - Prob. 2ECh. 8.7 - Prob. 3ECh. 8.7 - Prob. 4ECh. 8.7 - Prob. 5ECh. 8.7 - Prob. 6ECh. 8.7 - Prob. 7ECh. 8.7 - Prob. 8ECh. 8.7 - Prob. 9ECh. 8.7 - Prob. 10ECh. 8.7 - Prob. 11ECh. 8.7 - Prob. 12ECh. 8.7 - Prob. 13ECh. 8.7 - Prob. 14ECh. 8.7 - Prob. 15ECh. 8.7 - Prob. 16ECh. 8.7 - Prob. 17ECh. 8.7 - Prob. 18ECh. 8.7 - Preliminary work Use a table of integrals to...Ch. 8.7 - Prob. 20ECh. 8.7 - Preliminary work Use a table of integrals to...Ch. 8.7 - Prob. 22ECh. 8.7 - Prob. 23ECh. 8.7 - Prob. 24ECh. 8.7 - Prob. 25ECh. 8.7 - Prob. 26ECh. 8.7 - Prob. 27ECh. 8.7 - Prob. 28ECh. 8.7 - Prob. 29ECh. 8.7 - Prob. 30ECh. 8.7 - Preliminary work Use a table of integrals to...Ch. 8.7 - Prob. 32ECh. 8.7 - Prob. 33ECh. 8.7 - Prob. 34ECh. 8.7 - Prob. 35ECh. 8.7 - Prob. 36ECh. 8.7 - Prob. 37ECh. 8.7 - Prob. 38ECh. 8.7 - Prob. 39ECh. 8.7 - Prob. 40ECh. 8.7 - Prob. 41ECh. 8.7 - Prob. 42ECh. 8.7 - Prob. 43ECh. 8.7 - Prob. 44ECh. 8.7 - Prob. 45ECh. 8.7 - Prob. 46ECh. 8.7 - Prob. 47ECh. 8.7 - Prob. 48ECh. 8.7 - Prob. 65ECh. 8.7 - Prob. 66ECh. 8.7 - Prob. 67ECh. 8.7 - Prob. 68ECh. 8.7 - Prob. 71ECh. 8.7 - Prob. 72ECh. 8.7 - Prob. 73ECh. 8.7 - Prob. 74ECh. 8.7 - Apparent discrepancy Resolve the apparent...Ch. 8.7 - Prob. 83ECh. 8.7 - Prob. 84ECh. 8.7 - Prob. 86ECh. 8.8 - To apply the Midpoint Rule on the interval [3, 11]...Ch. 8.8 - Prob. 2QCCh. 8.8 - Prob. 3QCCh. 8.8 - Prob. 4QCCh. 8.8 - Prob. 5QCCh. 8.8 - Prob. 6QCCh. 8.8 - Prob. 1ECh. 8.8 - Prob. 2ECh. 8.8 - Prob. 3ECh. 8.8 - Prob. 4ECh. 8.8 - Prob. 5ECh. 8.8 - Prob. 6ECh. 8.8 - Prob. 7ECh. 8.8 - Prob. 8ECh. 8.8 - If the Trapezoid Rule is used on the interval [1,...Ch. 8.8 - Prob. 10ECh. 8.8 - Prob. 11ECh. 8.8 - Prob. 12ECh. 8.8 - Midpoint Rule approximations Find the indicated...Ch. 8.8 - Prob. 16ECh. 8.8 - Prob. 17ECh. 8.8 - Prob. 18ECh. 8.8 - Trapezoid Rule approximations Find the indicated...Ch. 8.8 - Trapezoid Rule approximations Find the indicated...Ch. 8.8 - Trapezoid Rule approximations Find the indicated...Ch. 8.8 - Trapezoid Rule approximations Find the indicated...Ch. 8.8 - Simpsons Rule approximations Find the indicated...Ch. 8.8 - Simpsons Rule approximations Find the indicated...Ch. 8.8 - Simpsons Rule approximations Find the indicated...Ch. 8.8 - Prob. 26ECh. 8.8 - Prob. 27ECh. 8.8 - Prob. 28ECh. 8.8 - Prob. 29ECh. 8.8 - Comparing the Midpoint and Trapezoid Rules Apply...Ch. 8.8 - Prob. 31ECh. 8.8 - Prob. 32ECh. 8.8 - Prob. 33ECh. 8.8 - Prob. 34ECh. 8.8 - Prob. 35ECh. 8.8 - Prob. 36ECh. 8.8 - Prob. 37ECh. 8.8 - Prob. 38ECh. 8.8 - Prob. 39ECh. 8.8 - Prob. 40ECh. 8.8 - Nonuniform grids Use the indicated methods to...Ch. 8.8 - Prob. 42ECh. 8.8 - Prob. 43ECh. 8.8 - Prob. 44ECh. 8.8 - Prob. 45ECh. 8.8 - Prob. 46ECh. 8.8 - Prob. 47ECh. 8.8 - Prob. 48ECh. 8.8 - Prob. 49ECh. 8.8 - Prob. 50ECh. 8.8 - Simpsons Rule Apply Simpsons Rule to the following...Ch. 8.8 - Prob. 52ECh. 8.8 - Explain why or why not Determine whether the...Ch. 8.8 - Prob. 54ECh. 8.8 - Prob. 55ECh. 8.8 - Prob. 56ECh. 8.8 - Prob. 57ECh. 8.8 - Prob. 58ECh. 8.8 - Prob. 59ECh. 8.8 - Prob. 60ECh. 8.8 - Prob. 61ECh. 8.8 - Prob. 62ECh. 8.8 - Prob. 63ECh. 8.8 - Prob. 64ECh. 8.8 - Prob. 65ECh. 8.8 - Prob. 66ECh. 8.8 - Estimating error Refer to Theorem 8.1 in the...Ch. 8.8 - Prob. 68ECh. 8.8 - Prob. 69ECh. 8.8 - Prob. 70ECh. 8.8 - Prob. 71ECh. 8.8 - Prob. 72ECh. 8.8 - Prob. 73ECh. 8.8 - Prob. 74ECh. 8.8 - Exact Simpsons Rule a. Use Simpsons Rule to...Ch. 8.8 - Prob. 76ECh. 8.8 - Trapezoid Rule and concavity Suppose f is positive...Ch. 8.8 - Prob. 78ECh. 8.8 - Prob. 79ECh. 8.9 - The function f(x) = 1 + x 1 decreases to 1 as x ....Ch. 8.9 - Prob. 2QCCh. 8.9 - Prob. 3QCCh. 8.9 - Prob. 4QCCh. 8.9 - What are the two general ways in which an improper...Ch. 8.9 - Evaluate 2dxx3 after writing the expression as a...Ch. 8.9 - Prob. 3ECh. 8.9 - Evaluate 01dxx1/5 after writing the integral as a...Ch. 8.9 - Write limaa0f(x)dx+limb0bf(x)dxas an improper...Ch. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Infinite intervals of integration Evaluate the...Ch. 8.9 - Prob. 10ECh. 8.9 - Infinite intervals of integration Evaluate the...Ch. 8.9 - Prob. 12ECh. 8.9 - Infinite intervals of integration Evaluate the...Ch. 8.9 - Prob. 14ECh. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Prob. 17ECh. 8.9 - Prob. 18ECh. 8.9 - Prob. 19ECh. 8.9 - Prob. 20ECh. 8.9 - Infinite intervals of integration Evaluate the...Ch. 8.9 - Infinite intervals of integration Evaluate the...Ch. 8.9 - Infinite intervals of integration Evaluate the...Ch. 8.9 - Prob. 24ECh. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Prob. 26ECh. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Prob. 28ECh. 8.9 - Prob. 29ECh. 8.9 - Prob. 30ECh. 8.9 - Infinite intervals of integration Evaluate the...Ch. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Prob. 33ECh. 8.9 - Prob. 34ECh. 8.9 - Prob. 35ECh. 8.9 - Infinite intervals of integration Evaluate the...Ch. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Prob. 40ECh. 8.9 - Integrals with unbounded integrands Evaluate the...Ch. 8.9 - Prob. 42ECh. 8.9 - Prob. 43ECh. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Prob. 46ECh. 8.9 - Integrals with unbounded integrands Evaluate the...Ch. 8.9 - Integrals with unbounded integrands Evaluate the...Ch. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Prob. 50ECh. 8.9 - Integrals with unbounded integrands Evaluate the...Ch. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Prob. 54ECh. 8.9 - Prob. 55ECh. 8.9 - Improper integrals Evaluate the following...Ch. 8.9 - Prob. 57ECh. 8.9 - Prob. 58ECh. 8.9 - Perpetual annuity Imagine that today you deposit B...Ch. 8.9 - Draining a pool Water is drained from a swimming...Ch. 8.9 - Bioavailability When a drug is given...Ch. 8.9 - Electronic chips Suppose the probability that a...Ch. 8.9 - Prob. 63ECh. 8.9 - Prob. 64ECh. 8.9 - Prob. 65ECh. 8.9 - Prob. 66ECh. 8.9 - Volumes on infinite intervals Find the volume of...Ch. 8.9 - Prob. 68ECh. 8.9 - Volumes on infinite intervals Find the volume of...Ch. 8.9 - Prob. 70ECh. 8.9 - Volumes with infinite integrands Find the volume...Ch. 8.9 - Prob. 72ECh. 8.9 - Prob. 73ECh. 8.9 - Prob. 74ECh. 8.9 - Volumes with infinite integrands Find the volume...Ch. 8.9 - Prob. 76ECh. 8.9 - Comparison Test Determine whether the following...Ch. 8.9 - Prob. 78ECh. 8.9 - Prob. 79ECh. 8.9 - Prob. 80ECh. 8.9 - Comparison Test Determine whether the following...Ch. 8.9 - Prob. 82ECh. 8.9 - Comparison Test Determine whether the following...Ch. 8.9 - Comparison Test Determine whether the following...Ch. 8.9 - Prob. 85ECh. 8.9 - Prob. 86ECh. 8.9 - Explain why or why not Determine whether the...Ch. 8.9 - Incorrect calculation a. What is wrong with this...Ch. 8.9 - Prob. 89ECh. 8.9 - Prob. 90ECh. 8.9 - Prob. 91ECh. 8.9 - Prob. 92ECh. 8.9 - Prob. 93ECh. 8.9 - Prob. 94ECh. 8.9 - Prob. 95ECh. 8.9 - Prob. 96ECh. 8.9 - Prob. 97ECh. 8.9 - Prob. 98ECh. 8.9 - Prob. 99ECh. 8.9 - Prob. 100ECh. 8.9 - Many methods needed Show that 0xlnx(1+x)2dx = in...Ch. 8.9 - Prob. 102ECh. 8.9 - Prob. 103ECh. 8.9 - Prob. 104ECh. 8.9 - Prob. 105ECh. 8.9 - Prob. 106ECh. 8.9 - Prob. 107ECh. 8.9 - Prob. 108ECh. 8.9 - Prob. 109ECh. 8.9 - Prob. 110ECh. 8.9 - Prob. 111ECh. 8.9 - Prob. 112ECh. 8 - Explain why or why not Determine whether the...Ch. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - Prob. 5RECh. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Prob. 31RECh. 8 - Integration techniques Use the methods introduced...Ch. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Prob. 36RECh. 8 - Partial fractions Use partial fractions to...Ch. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Prob. 40RECh. 8 - Prob. 41RECh. 8 - Prob. 42RECh. 8 - Prob. 43RECh. 8 - Prob. 44RECh. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Prob. 50RECh. 8 - Prob. 51RECh. 8 - Prob. 52RECh. 8 - Prob. 53RECh. 8 - Prob. 54RECh. 8 - Prob. 55RECh. 8 - Prob. 56RECh. 8 - Prob. 57RECh. 8 - Prob. 58RECh. 8 - Prob. 59RECh. 8 - Prob. 60RECh. 8 - Prob. 61RECh. 8 - Prob. 62RECh. 8 - Prob. 63RECh. 8 - Miscellaneous Integrals Evaluate the following...Ch. 8 - Prob. 65RECh. 8 - Prob. 66RECh. 8 - Prob. 67RECh. 8 - Prob. 68RECh. 8 - Preliminary work Make a change of variables or use...Ch. 8 - Prob. 70RECh. 8 - Prob. 71RECh. 8 - Prob. 72RECh. 8 - Prob. 73RECh. 8 - Prob. 74RECh. 8 - Prob. 75RECh. 8 - Prob. 76RECh. 8 - Prob. 77RECh. 8 - Prob. 78RECh. 8 - Prob. 79RECh. 8 - Prob. 80RECh. 8 - Prob. 81RECh. 8 - Improper integrals Evaluate the following...Ch. 8 - Prob. 83RECh. 8 - Prob. 84RECh. 8 - Improper integrals Evaluate the following...Ch. 8 - Improper integrals Evaluate the following...Ch. 8 - Prob. 87RECh. 8 - Prob. 88RECh. 8 - Prob. 89RECh. 8 - Prob. 90RECh. 8 - Prob. 91RECh. 8 - Prob. 92RECh. 8 - Prob. 93RECh. 8 - Prob. 94RECh. 8 - Numerical integration Estimate the following...Ch. 8 - Prob. 96RECh. 8 - Numerical integration Estimate the following...Ch. 8 - Prob. 98RECh. 8 - Improper integrals by numerical methods Use the...Ch. 8 - Prob. 100RECh. 8 - Prob. 101RECh. 8 - Prob. 102RECh. 8 - Prob. 103RECh. 8 - Prob. 104RECh. 8 - Prob. 105RECh. 8 - Prob. 106RECh. 8 - Prob. 107RECh. 8 - Prob. 108RECh. 8 - Prob. 109RECh. 8 - Comparing distances Starting at the same time and...Ch. 8 - Prob. 111RECh. 8 - Prob. 112RECh. 8 - Prob. 113RECh. 8 - Arc length of the natural logarithm Consider the...Ch. 8 - Prob. 115RECh. 8 - Prob. 116RECh. 8 - Prob. 117RECh. 8 - Prob. 118RECh. 8 - Comparing volumes Let R be the region bounded by y...Ch. 8 - Prob. 120RECh. 8 - Prob. 121RECh. 8 - Prob. 122RECh. 8 - Prob. 123RECh. 8 - Prob. 124RECh. 8 - Prob. 125RE
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