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Math
Calculus
Calculus: Early Transcendentals, Enhanced Etext
Chapter 5.9, Problem 74ES
Chapter 5.9, Problem 74ES
BUY
Calculus: Early Transcendentals, Enhanced Etext
12th Edition
ISBN:
9781119777984
Author: Howard Anton; Irl C. Bivens; Stephen Davis
Publisher:
Wiley Global Education US
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1 Limits And Continuity
2 The Derivative
3 Topics In Differentiation
4 The Derivative In Graphing And Applications
5 Integration
6 Applications Of The Definite Integral In Geometry, Science, And Engineering
7 Principles Of Integral Evaluation
8 Mathematical Modeling With Differential Equations
9 Infinite Series
10 Parametric And Polar Curves; Conic Sections
11 Three-dimensional Space; Vectors
12 Vector-valued Functions
13 Partial Derivatives
14 Multiple Integrals
15 Topics In Vector Calculus
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5.1 An Overview Of The Area Problem
5.2 The Indefinite Integral
5.3 Integration By Substitution
5.4 The Definition Of Area As A Limit; Sigma Notation
5.5 The Definite Integral
5.6 The Fundamental Theorem Of Calculus
5.7 Rectilinear Motion Revisited Using Integration
5.8 Average Value Of A Function And Its Applications
5.9 Evaluating Definite Integrals By Substitution
5.10 Logarithmic And Other Functions Defined By Integrals
Chapter Questions
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Problem 1QCE: Assume that g is continuous on a,b and that f is continuous on an interval containing the values of...
Problem 2QCE: In each part, use the substitution to replace the given integral with an integral involving the...
Problem 3QCE: Evaluate the integral by making an appropriate substitution. (a) 0sin3xdx= (b) 23xx22dx= (c)...
Problem 1ES: Express the integral in terms of the variable u , but do not evaluate it. (a) 132x13dx;u=2x1 (b)...
Problem 2ES: Express the integral in terms of the variable u , but do not evaluate it. (a) 1452x8dx;u=52x (b)...
Problem 3ES: Express the integral in terms of the variable u , but do not evaluate it. (a) 01e2x1dx;u=2x1 (b)...
Problem 4ES: Express the integral in terms of the variable u , but do not evaluate it. (a) 13tan1x1+x2dx;u=tan1x...
Problem 5ES: Evaluate the definite integral two ways: first by a u- substitution in the definite integral and...
Problem 6ES: Evaluate the definite integral two ways: first by a u- substitution in the definite integral and...
Problem 7ES: Evaluate the definite integral two ways: first by a u- substitution in the definite integral and...
Problem 8ES: Evaluate the definite integral two ways: first by a u- substitution in the definite integral and...
Problem 9ES: Evaluate the definite integral two ways: first by a u- substitution in the definite integral and...
Problem 10ES: Evaluate the definite integral two ways: first by a u- substitution in the definite integral and...
Problem 11ES: Evaluate the definite integral two ways: first by a u- substitution in the definite integral and...
Problem 12ES
Problem 13ES
Problem 14ES
Problem 15ES: Evaluate the definite integral two ways: first by a u- substitution in the definite integral and...
Problem 16ES
Problem 17ES: Evaluate the definite integral two ways: first by a u- substitution in the definite integral and...
Problem 18ES
Problem 19ES: Evaluate the definite integral by expressing it in terms of u and evaluating the resulting integral...
Problem 20ES: Evaluate the definite integral by expressing it in terms of u and evaluating the resulting integral...
Problem 21ES: Evaluate the definite integral by expressing it in terms of u and evaluating the resulting integral...
Problem 22ES: Evaluate the definite integral by expressing it in terms of u and evaluating the resulting integral...
Problem 23ES: A particle moves with a velocity of t=sintm/s along an s-axis . Find the distance traveled by the...
Problem 24ES
Problem 25ES: Find the area under the curve y=9/x+22 over the interval 1,1 .
Problem 26ES
Problem 27ES: Find the area of the region enclosed by the graphs of y=1/19x2,y=0,x=0, and x=16 .
Problem 28ES
Problem 29ES: Find the average value of fx=x/5x2+12 over the interval 0,2 .
Problem 30ES
Problem 31ES: Evaluate the integrals by any method. 15dx2x1
Problem 32ES: Evaluate the integrals by any method. 125x1dx
Problem 33ES: Evaluate the integrals by any method. 11x2dxx3+9
Problem 34ES: Evaluate the integrals by any method. /26sinxcosx+15dx
Problem 35ES: Evaluate the integrals by any method. 13x+2x2+4x+7dx
Problem 36ES
Problem 37ES: Evaluate the integrals by any method. 0/44sinxcosxdx
Problem 38ES
Problem 39ES: Evaluate the integrals by any method. 05xcosx2dx
Problem 40ES
Problem 41ES: Evaluate the integrals by any method. /12/9sec23d
Problem 42ES
Problem 43ES: Evaluate the integrals by any method. 01y2dy43y
Problem 44ES
Problem 45ES
Problem 46ES: Evaluate the integrals by any method. 12xex2dx
Problem 47ES: Evaluate the integrals by any method. 01x43x4dx
Problem 48ES: Evaluate the integrals by any method. 121x4xdx
Problem 49ES
Problem 50ES: Evaluate the integrals by any method. 12x3+x4dx
Problem 51ES: (a) Use a CAS to find the exact value of the integral 0/6sin4xcos3xdx (b) Confirm the exact value of...
Problem 52ES: (a) Use a CAS to find the exact value of the integral /4/4tan4xdx (b) Confirm the exact value of...
Problem 53ES: (a) Find 01f3x+1dx if 14fxdx=5 . (b) Find 03f3xdx if 09fxdx=5 . (c) Find 20xfx2dx if 04fxdx=1 .
Problem 54ES: Given that m and n are positive integers, show that 01xm1xndx=01xn1xmdx by making a substitution. Do...
Problem 55ES: Given that n is a positive integers, show that 0/2sinnxdx=0/2cosnxdx by using a trigonometric...
Problem 56ES: Given that n is a positive integer, evaluate the integral 01x1xndx
Problem 57ES: Medication can be administered to a patient in different ways. For a given method, let ct denote the...
Problem 58ES: Medication can be administered to a patient in different ways. For a given method, let ct denote the...
Problem 59ES: Medication can be administered to a patient in different ways. For a given method, let ct denote the...
Problem 60ES: Medication can be administered to a patient in different ways. For a given method, let ct denote the...
Problem 61ES: Suppose that at time t=0 there are 750 bacteria in a growth medium and the bacteria population yt...
Problem 62ES: Suppose that a particle moving along a coordinate line has velocity t=25+10e0.05tft/s . (a) What is...
Problem 63ES
Problem 64ES: Electricity is supplied to homes in the form of alternating current, which means that the voltage...
Problem 65ES: Find a positive value of k such that the area under the graph of y=e2x over the interval 0,k is 3...
Problem 66ES: Use a graphing utility to estimate the value of kk0 so that the region enclosed by y=1/1+kx2,y=0,x=0...
Problem 67ES: (a) Find the limit limn+k=1nsink/nn by evaluating an appropriate definite integral over the interval...
Problem 68ES: Let I=1111+x2dx (a) Explain why I0 . (b) Show that the substitution x=1/u results in I=1111+x2dx=I...
Problem 69ES: (a) Prove that if f is an odd function, then aafxdx=0 (b) Prove that if f is an even function, then...
Problem 70ES: Show that if f and g are continuous functions, then 0tftxgxdx=0tfxgtxdx
Problem 71ES: (a) Let I=0afxfx+faxdx Show that I=a/2 . (b) Use the result of part (a) to find 03xx+3xdx (c) Use...
Problem 72ES: Evaluate (a) 11xcosx2dx (b) 0sin8xcos5xdx
Problem 73ES
Problem 74ES
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CONCEPT CHECK Determine whether each of the following statements is true or false, and explain why. Substitution can often be used to turn a complicated integral into a simpler one.
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