CODE/CALC ET 3-HOLE
2nd Edition
ISBN: 9781323178522
Author: Briggs
Publisher: PEARSON
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Chapter 5.5, Problem 12E
To determine
To find: The antiderivative of
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Find an antiderivative of the following function.
7
p(z) = (VE)
An antiderivative is
Activity 1
Find the antiderivative of the following functions. Show your complete solution and emphasize the final
answer. (Do not forget to write your name and section on your answer sheet.)
1. S 2x²dx
2. J금ax
3. fx*(5 – x²)dx
4. A dx
cos x
3 tan x-4 cos²x
5.
dx
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Find the most general antiderivative of the functions. Leave answers with positive
exponents.
f (v) = 4Vv – 3v²
,3/2
2.
Chapter 5 Solutions
CODE/CALC ET 3-HOLE
Ch. 5.1 - Suppose an object moves along a line at 15 m/s,...Ch. 5.1 - Given the graph of the positive velocity of an...Ch. 5.1 - Prob. 3ECh. 5.1 - Explain how Riemann sum approximations to the area...Ch. 5.1 - Suppose the interval [1, 3] is partitioned into n...Ch. 5.1 - Prob. 6ECh. 5.1 - Does a right Riemann sum underestimate or...Ch. 5.1 - Does a left Riemann sum underestimate or...Ch. 5.1 - Approximating displacement The velocity in ft/s of...Ch. 5.1 - Approximating displacement The velocity in ft/s of...
Ch. 5.1 - Approximating displacement The velocity of an...Ch. 5.1 - Approximating displacement The velocity of an...Ch. 5.1 - Approximating displacement The velocity of an...Ch. 5.1 - Approximating displacement The velocity of an...Ch. 5.1 - Approximating displacement The velocity of an...Ch. 5.1 - Approximating displacement The velocity of an...Ch. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - A midpoint Riemann sum Approximate the area of the...Ch. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Midpoint Riemann sums Complete the following steps...Ch. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Riemann sums from tables Evaluate the left and...Ch. 5.1 - Prob. 36ECh. 5.1 - Displacement from a table of velocities The...Ch. 5.1 - Displacement from a table of velocities The...Ch. 5.1 - Sigma notation Express the following sums using...Ch. 5.1 - Sigma notation Express the following sums using...Ch. 5.1 - Sigma notation Evaluate the following expressions....Ch. 5.1 - Evaluating sums Evaluate the following expressions...Ch. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Explain why or why not Determine whether the...Ch. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Prob. 60ECh. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Approximating areas Estimate the area of the...Ch. 5.1 - Prob. 64ECh. 5.1 - Prob. 65ECh. 5.1 - Prob. 66ECh. 5.1 - Displacement from a velocity graph Consider the...Ch. 5.1 - Flow rates Suppose a gauge at the outflow of a...Ch. 5.1 - Mass from density A thin 10-cm rod is made of an...Ch. 5.1 - Prob. 70ECh. 5.1 - Prob. 71ECh. 5.1 - Prob. 72ECh. 5.1 - Prob. 73ECh. 5.1 - Prob. 74ECh. 5.1 - Prob. 75ECh. 5.1 - Riemann sums for constant functions Let f(x) = c,...Ch. 5.1 - Prob. 77ECh. 5.1 - Prob. 78ECh. 5.1 - Prob. 79ECh. 5.2 - What does net area measure?Ch. 5.2 - Prob. 2ECh. 5.2 - Under what conditions does the net area of a...Ch. 5.2 - Prob. 4ECh. 5.2 - Use graphs to evaluate 02sinxdx and 02cosxdx.Ch. 5.2 - Explain how the notation for Riemann sums,...Ch. 5.2 - Give a geometrical explanation of why aaf(x)dx=0.Ch. 5.2 - Use Table 5.4 to rewrite 16(2x34x)dx as the...Ch. 5.2 - Use geometry to find a formula for 0axdx, in terms...Ch. 5.2 - If f is continuous on [a, b] and abf(x)dx=0, what...Ch. 5.2 - Approximating net area The following functions are...Ch. 5.2 - Approximating net area The following functions are...Ch. 5.2 - Approximating net area The following functions are...Ch. 5.2 - Approximating net area The following functions are...Ch. 5.2 - Approximating net area The following functions are...Ch. 5.2 - Approximating net area The following functions are...Ch. 5.2 - Approximating net area The following functions are...Ch. 5.2 - Approximating net area The following functions are...Ch. 5.2 - Approximating net area The following functions are...Ch. 5.2 - Approximating net area The following functions are...Ch. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Identifying definite integrals as limits of sums...Ch. 5.2 - Prob. 24ECh. 5.2 - Net area and definite integrals Use geometry (not...Ch. 5.2 - Net area and definite integrals Use geometry (not...Ch. 5.2 - Net area and definite integrals Use geometry (not...Ch. 5.2 - Net area and definite integrals Use geometry (not...Ch. 5.2 - Net area and definite integrals Use geometry (not...Ch. 5.2 - Net area and definite integrals Use geometry (not...Ch. 5.2 - Net area and definite integrals Use geometry (not...Ch. 5.2 - Net area and definite integrals Use geometry (not...Ch. 5.2 - Net area from graphs The figure shows the areas of...Ch. 5.2 - Net area from graphs The figure shows the areas of...Ch. 5.2 - Net area from graphs The figure shows the areas of...Ch. 5.2 - Net area from graphs The figure shows the areas of...Ch. 5.2 - Net area from graphs The accompanying figure shows...Ch. 5.2 - Net area from graphs The accompanying figure shows...Ch. 5.2 - Net area from graphs The accompanying figure shows...Ch. 5.2 - Net area from graphs The accompanying figure shows...Ch. 5.2 - Properties of integrals Use only the fact that...Ch. 5.2 - Properties of integrals Suppose 14f(x)dx=8 and...Ch. 5.2 - Properties of integrals Suppose 03f(x)dx=2,...Ch. 5.2 - Properties of integrals Suppose f(x) 0 on [0, 2],...Ch. 5.2 - Using properties of integrals Use the value of the...Ch. 5.2 - Using properties of integrals Use the value of the...Ch. 5.2 - Limits of sums Use the definition of the definite...Ch. 5.2 - Limits of sums Use the definition of the definite...Ch. 5.2 - Limits of sums Use the definition of the definite...Ch. 5.2 - Limits of sums Use the definition of the definite...Ch. 5.2 - Limits of sums Use the definition of the definite...Ch. 5.2 - Limits of sums Use the definition of the definite...Ch. 5.2 - Explain why or why not Determine whether the...Ch. 5.2 - Approximating definite integrals Complete the...Ch. 5.2 - Approximating definite integrals Complete the...Ch. 5.2 - Approximating definite integrals Complete the...Ch. 5.2 - Approximating definite integrals Complete the...Ch. 5.2 - Approximating definite integrals with a calculator...Ch. 5.2 - Prob. 59ECh. 5.2 - Prob. 60ECh. 5.2 - Approximating definite integrals with a calculator...Ch. 5.2 - Prob. 62ECh. 5.2 - Midpoint Riemann sums with a calculator Consider...Ch. 5.2 - Midpoint Riemann sums with a calculator Consider...Ch. 5.2 - Midpoint Riemann sums with a calculator Consider...Ch. 5.2 - Prob. 66ECh. 5.2 - More properties of integrals Consider two...Ch. 5.2 - Prob. 68ECh. 5.2 - Prob. 69ECh. 5.2 - Prob. 70ECh. 5.2 - Prob. 71ECh. 5.2 - Area by geometry Use geometry to evaluate the...Ch. 5.2 - Area by geometry Use geometry to evaluate the...Ch. 5.2 - Prob. 74ECh. 5.2 - Area by geometry Use geometry to evaluate the...Ch. 5.2 - Integrating piecewise continuous functions Suppose...Ch. 5.2 - Prob. 77ECh. 5.2 - Prob. 78ECh. 5.2 - Prob. 79ECh. 5.2 - Prob. 80ECh. 5.2 - Constants in integrals Use the definition of the...Ch. 5.2 - Zero net area If 0 c d, then find the value of b...Ch. 5.2 - A nonintegrable function Consider the function...Ch. 5.2 - Powers of x by Riemann sums Consider the integral...Ch. 5.2 - An exact integration formula Evaluate abdxx2,...Ch. 5.3 - Suppose A is an area function of f. What is the...Ch. 5.3 - Suppose F is an antiderivative of f and A is an...Ch. 5.3 - Explain in words and write mathematically how the...Ch. 5.3 - Let f(x) = c, where c is a positive constant....Ch. 5.3 - The linear function f(x) = 3 x is decreasing on...Ch. 5.3 - Evaluate 023x2dx and 223x2dx.Ch. 5.3 - Explain in words and express mathematically the...Ch. 5.3 - Why can the constant of integration be omitted...Ch. 5.3 - Evaluate ddxaxf(t)dt and ddxabf(t)dt, where a and...Ch. 5.3 - Explain why abf(x)dx=f(b)f(a).Ch. 5.3 - Prob. 11ECh. 5.3 - Area functions The graph of f is shown in the...Ch. 5.3 - Area functions for constant functions Consider the...Ch. 5.3 - Area functions for constant functions Consider the...Ch. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Area functions for the same linear function Let...Ch. 5.3 - Area functions for the same linear function Let...Ch. 5.3 - Area functions for linear functions Consider the...Ch. 5.3 - Area functions for linear functions Consider the...Ch. 5.3 - Area functions for linear functions Consider the...Ch. 5.3 - Area functions for linear functions Consider the...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Prob. 46ECh. 5.3 - Prob. 47ECh. 5.3 - Prob. 48ECh. 5.3 - Definite integrals Evaluate the following...Ch. 5.3 - Prob. 50ECh. 5.3 - Areas Find (i) the net area and (ii) the area of...Ch. 5.3 - Areas Find (i) the net area and (ii) the area of...Ch. 5.3 - Areas Find (i) the net area and (ii) the area of...Ch. 5.3 - Areas Find (i) the net area and (ii) the area of...Ch. 5.3 - Areas of regions Find the area of the region...Ch. 5.3 - Areas of regions Find the area of the region...Ch. 5.3 - Areas of regions Find the area of the region...Ch. 5.3 - Areas of regions Find the area of the region...Ch. 5.3 - Areas of regions Find the area of the region...Ch. 5.3 - Areas of regions Find the area of the region...Ch. 5.3 - Derivatives of integrals Simplify the following...Ch. 5.3 - Derivatives of integrals Simplify the following...Ch. 5.3 - Derivatives of integrals Simplify the following...Ch. 5.3 - Prob. 64ECh. 5.3 - Derivatives of integrals Simplify the following...Ch. 5.3 - Derivatives of integrals Simplify the following...Ch. 5.3 - Prob. 67ECh. 5.3 - Derivatives of integrals Simplify the following...Ch. 5.3 - Prob. 69ECh. 5.3 - Working with area functions Consider the function...Ch. 5.3 - Prob. 71ECh. 5.3 - Prob. 72ECh. 5.3 - Prob. 73ECh. 5.3 - Prob. 74ECh. 5.3 - Area functions from graphs The graph of f is given...Ch. 5.3 - Prob. 76ECh. 5.3 - Working with area functions Consider the function...Ch. 5.3 - Working with area functions Consider the function...Ch. 5.3 - Prob. 79ECh. 5.3 - Prob. 80ECh. 5.3 - Prob. 81ECh. 5.3 - Prob. 82ECh. 5.3 - Prob. 83ECh. 5.3 - Prob. 84ECh. 5.3 - Explain why or why not Determine whether the...Ch. 5.3 - Definite integrals Evaluate the following definite...Ch. 5.3 - Definite integrals Evaluate the following definite...Ch. 5.3 - Prob. 88ECh. 5.3 - Definite integrals Evaluate the following definite...Ch. 5.3 - Prob. 90ECh. 5.3 - Definite integrals Evaluate the following definite...Ch. 5.3 - Definite integrals Evaluate the following definite...Ch. 5.3 - Definite integrals Evaluate the following definite...Ch. 5.3 - Prob. 94ECh. 5.3 - Areas of regions Find the area of the region R...Ch. 5.3 - Prob. 96ECh. 5.3 - Areas of regions Find the area of the region R...Ch. 5.3 - Areas of regions Find the area of the region R...Ch. 5.3 - Prob. 99ECh. 5.3 - Derivatives and integrals Simplify the given...Ch. 5.3 - Derivatives and integrals Simplify the given...Ch. 5.3 - Derivatives and integrals Simplify the given...Ch. 5.3 - Derivatives and integrals Simplify the given...Ch. 5.3 - Derivatives and integrals Simplify the given...Ch. 5.3 - Prob. 105ECh. 5.3 - Cubic zero net area Consider the graph of the...Ch. 5.3 - Maximum net area What value of b 1 maximizes the...Ch. 5.3 - Maximum net area Graph the function f(x) = 8 + 2x ...Ch. 5.3 - An integral equation Use the Fundamental Theorem...Ch. 5.3 - Prob. 110ECh. 5.3 - Asymptote of sine integral Use a calculator to...Ch. 5.3 - Sine integral Show that the sine integral...Ch. 5.3 - Prob. 113ECh. 5.3 - Prob. 114ECh. 5.3 - Discrete version of the Fundamental Theorem In...Ch. 5.3 - Continuity at the endpoints Assume that f is...Ch. 5.4 - If f is an odd function, why is aaf(x)dx=0?Ch. 5.4 - If f is an even function, why is...Ch. 5.4 - Is x12 an even or odd function? Is sin x2 an even...Ch. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - Prob. 6ECh. 5.4 - Symmetry in integrals Use symmetry to evaluate the...Ch. 5.4 - Symmetry in integrals Use symmetry to evaluate the...Ch. 5.4 - Symmetry in integrals Use symmetry to evaluate the...Ch. 5.4 - Symmetry in integrals Use symmetry to evaluate the...Ch. 5.4 - Symmetry in integrals Use symmetry to evaluate the...Ch. 5.4 - Symmetry in integrals Use symmetry to evaluate the...Ch. 5.4 - Symmetry in integrals Use symmetry to evaluate the...Ch. 5.4 - Symmetry in integrals Use symmetry to evaluate the...Ch. 5.4 - Prob. 15ECh. 5.4 - Symmetry in integrals Use symmetry to evaluate the...Ch. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - Prob. 19ECh. 5.4 - Prob. 20ECh. 5.4 - Average values Find the average value of the...Ch. 5.4 - Average values Find the average value of the...Ch. 5.4 - Average values Find the average value of the...Ch. 5.4 - Average values Find the average value of the...Ch. 5.4 - Average values Find the average value of the...Ch. 5.4 - Prob. 26ECh. 5.4 - Average values Find the average value of the...Ch. 5.4 - Average values Find the average value of the...Ch. 5.4 - Average values Find the average value of the...Ch. 5.4 - Average values Find the average value of the...Ch. 5.4 - Average distance on a parabola What is the average...Ch. 5.4 - Average elevation The elevation of a path is given...Ch. 5.4 - Average height of an arch The height of an arch...Ch. 5.4 - Average height of a wave The surface of a water...Ch. 5.4 - Mean Value Theorem for Integrals Find or...Ch. 5.4 - Mean Value Theorem for Integrals Find or...Ch. 5.4 - Mean Value Theorem for Integrals Find or...Ch. 5.4 - Mean Value Theorem for Integrals Find or...Ch. 5.4 - Mean Value Theorem for Integrals Find or...Ch. 5.4 - Mean Value Theorem for Integrals Find or...Ch. 5.4 - Explain why or why not Determine whether the...Ch. 5.4 - Prob. 42ECh. 5.4 - Symmetry in integrals Use symmetry to evaluate the...Ch. 5.4 - Symmetry in integrals Use symmetry to evaluate the...Ch. 5.4 - Symmetry in integrals Use symmetry to evaluate the...Ch. 5.4 - Prob. 46ECh. 5.4 - Gateway Arch The Gateway Arch in St. Louis is 630...Ch. 5.4 - Another Gateway Arch Another description of the...Ch. 5.4 - Prob. 49ECh. 5.4 - Comparing a sine and a quadratic function Consider...Ch. 5.4 - Using symmetry Suppose f is an even function and...Ch. 5.4 - Using symmetry Suppose f is an odd function,...Ch. 5.4 - Symmetry of composite functions Prove that the...Ch. 5.4 - Symmetry of composite functions Prove that the...Ch. 5.4 - Prob. 55ECh. 5.4 - Symmetry of composite functions Prove that the...Ch. 5.4 - Prob. 57ECh. 5.4 - Prob. 58ECh. 5.4 - Problems of antiquity Several calculus problems...Ch. 5.4 - Prob. 60ECh. 5.4 - Prob. 61ECh. 5.4 - Prob. 62ECh. 5.4 - A sine integral by Riemann sums Consider the...Ch. 5.4 - Alternative definitions of means Consider the...Ch. 5.4 - Symmetry of powers Fill in the following table...Ch. 5.4 - Prob. 66ECh. 5.4 - Prob. 67ECh. 5.4 - Bounds on an integral Suppose f is continuous on...Ch. 5.4 - Generalizing the Mean Value Theorem for Integrals...Ch. 5.5 - Review Questions 1. On which derivative rule is...Ch. 5.5 - Why is the Substitution Rule referred to as a...Ch. 5.5 - The composite function f(g(x)) consists of an...Ch. 5.5 - Find a suitable substitution for evaluating...Ch. 5.5 - When using a change of variables u = g(x) to...Ch. 5.5 - If the change of variables u = x2 4 is used to...Ch. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.5 - Prob. 10ECh. 5.5 - Prob. 11ECh. 5.5 - Prob. 12ECh. 5.5 - Substitution given Use the given substitution to...Ch. 5.5 - Substitution given Use the given substitution to...Ch. 5.5 - Substitution given Use the given substitution to...Ch. 5.5 - Substitution given Use the given substitution to...Ch. 5.5 - Indefinite integrals Use a change of variables to...Ch. 5.5 - Indefinite integrals Use a change of variables to...Ch. 5.5 - Indefinite integrals Use a change of variables to...Ch. 5.5 - Prob. 20ECh. 5.5 - Prob. 21ECh. 5.5 - Indefinite integrals Use a change of variables to...Ch. 5.5 - Indefinite integrals Use a change of variables to...Ch. 5.5 - Indefinite integrals Use a change of variables to...Ch. 5.5 - Prob. 25ECh. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - Prob. 28ECh. 5.5 - Prob. 29ECh. 5.5 - Prob. 30ECh. 5.5 - Prob. 31ECh. 5.5 - Indefinite integrals Use a change of variables to...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Definite integrals Use a change of variables to...Ch. 5.5 - Definite integrals Use a change of variables to...Ch. 5.5 - Definite integrals Use a change of variables to...Ch. 5.5 - Definite integrals Use a change of variables to...Ch. 5.5 - Definite integrals Use a change of variables to...Ch. 5.5 - Definite integrals Use a change of variables to...Ch. 5.5 - Definite integrals Use a change of variables to...Ch. 5.5 - Definite integrals Use a change of variables to...Ch. 5.5 - Definite integrals Use a change of variables to...Ch. 5.5 - Definite integrals Use a change of variables to...Ch. 5.5 - Definite integrals Use a change of variables to...Ch. 5.5 - Prob. 50ECh. 5.5 - Prob. 51ECh. 5.5 - Definite integrals Use a change of variables to...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Prob. 60ECh. 5.5 - Explain why or why not Determine whether the...Ch. 5.5 - Additional integrals Use a change of variables to...Ch. 5.5 - Prob. 63ECh. 5.5 - Prob. 64ECh. 5.5 - Prob. 65ECh. 5.5 - Prob. 66ECh. 5.5 - Prob. 67ECh. 5.5 - Prob. 68ECh. 5.5 - Prob. 69ECh. 5.5 - Prob. 70ECh. 5.5 - Additional integrals Use a change of variables to...Ch. 5.5 - Prob. 72ECh. 5.5 - Prob. 73ECh. 5.5 - Prob. 74ECh. 5.5 - Prob. 75ECh. 5.5 - Prob. 76ECh. 5.5 - Prob. 77ECh. 5.5 - Prob. 78ECh. 5.5 - Prob. 79ECh. 5.5 - Prob. 80ECh. 5.5 - Areas of regions Find the area of the following...Ch. 5.5 - Prob. 82ECh. 5.5 - Prob. 83ECh. 5.5 - Prob. 84ECh. 5.5 - Substitutions Suppose that p is a nonzero real...Ch. 5.5 - Periodic motion An object moves along a line with...Ch. 5.5 - Population models The population of a culture of...Ch. 5.5 - Prob. 88ECh. 5.5 - Average value of sine functions Use a graphing...Ch. 5.5 - Looking ahead: Integrals of tan x and cot x Use a...Ch. 5.5 - Looking ahead: Integrals of sec x and csc x a....Ch. 5.5 - Equal areas The area of the shaded region under...Ch. 5.5 - Equal areas The area of the shaded region under...Ch. 5.5 - Prob. 94ECh. 5.5 - Prob. 95ECh. 5.5 - Prob. 96ECh. 5.5 - Prob. 97ECh. 5.5 - Prob. 98ECh. 5.5 - More than one way Occasionally, two different...Ch. 5.5 - Prob. 100ECh. 5.5 - Prob. 101ECh. 5.5 - sin2 ax and cos2 ax integrals Use the Substitution...Ch. 5.5 - Integral of sin2 x cos2 x Consider the integral...Ch. 5.5 - Substitution: shift Perhaps the simplest change of...Ch. 5.5 - Prob. 105ECh. 5.5 - Prob. 106ECh. 5.5 - Prob. 107ECh. 5.5 - Prob. 108ECh. 5.5 - Prob. 109ECh. 5.5 - Prob. 110ECh. 5.5 - Multiple substitutions If necessary, use two or...Ch. 5 - Explain why or why not Determine whether the...Ch. 5 - Velocity to displacement An object travels on the...Ch. 5 - Area by geometry Use geometry to evaluate the...Ch. 5 - Displacement by geometry Use geometry to find the...Ch. 5 - Area by geometry Use geometry to evaluate...Ch. 5 - Prob. 6RECh. 5 - Integration by Riemann sums Consider the integral...Ch. 5 - Limit definition of the definite integral Use the...Ch. 5 - Limit definition of the definite integral Use the...Ch. 5 - Limit definition of the definite integral Use the...Ch. 5 - Prob. 11RECh. 5 - Prob. 12RECh. 5 - Sum to integral Evaluate the following limit by...Ch. 5 - Area function by geometry Use geometry to find the...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Prob. 17RECh. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Prob. 31RECh. 5 - Area of regions Compute the area of the region...Ch. 5 - Prob. 33RECh. 5 - Prob. 34RECh. 5 - Prob. 35RECh. 5 - Area versus net area Find (i) the net area and...Ch. 5 - Symmetry properties Suppose that 04f(x)dx=10 and...Ch. 5 - Prob. 38RECh. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Displacement from velocity A particle moves along...Ch. 5 - Average height A baseball is launched into the...Ch. 5 - Average values Integration is not needed. a. Find...Ch. 5 - Prob. 48RECh. 5 - An unknown function Assume f is continuous on [2,...Ch. 5 - Prob. 50RECh. 5 - Prob. 51RECh. 5 - Prob. 52RECh. 5 - Ascent rate of a scuba diver Divers who ascend too...Ch. 5 - Prob. 54RECh. 5 - Prob. 55RECh. 5 - Area functions and the Fundamental Theorem...Ch. 5 - Limits with integrals Evaluate the following...Ch. 5 - Limits with integrals Evaluate the following...Ch. 5 - Prob. 59RECh. 5 - Change of variables Use the change of variables u3...Ch. 5 - Inverse tangent integral Prove that for nonzero...Ch. 5 - Prob. 62RECh. 5 - Prob. 63RECh. 5 - Prob. 64RECh. 5 - Prob. 65RECh. 5 - Prob. 66RECh. 5 - Prob. 67RECh. 5 - Area with a parameter Let a 0 be a real number...Ch. 5 - Equivalent equations Explain why if a function u...Ch. 5 - Prob. 70RECh. 5 - Prob. 71RECh. 5 - Exponential inequalities Sketch a graph of f(t) =...
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- Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.arrow_forwardRepeat the previous exercise to find the formula forthe APY of an account that compounds daily. Usethe results from this and the previous exercise todevelop a function I(n)for the APY of any accountthat compounds n times per year.arrow_forwardFind the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and y=5, then z=28.arrow_forward
- Differentiate the function. 6. 2. y=- + 2. TC %3D x² +1 Choose the correct setup below to differentiate the function. d. d. (x² + 1) • (2) + 2 (x² + 1) d. 9. dx dx y' = xp 2. TC 2. d (x² +1). ) ( +1) (6(x²+1) + 2m) = (6(x + 1) + 2n dx y' = %3D (x² + 1)? (x² + 1) ax" (2) – 2. (x² + 1) 2+1) dx 6. y' = dx (x² + 1)² TC (x2+1).유 (6(x2+ 1) +2m) + (6(x2+1)+ 2x). ( (6(x² +1) + 27) + (6(x² + 1) + 2x) (x²+1) dx y' = - (x² + 1)² (x²+1)· dx 2) - 2. dx (x² + 1) d. y' = 6. TC (2)2arrow_forwardDifferentiate the function. y = (7x - x+4) ( - x° + 5) y' =D %3D ur Enter your answer in the answer box. 8:00am here to search Larrow_forwardAn object travels with velocity function given by v (t) = 3t + 5. The next three questions refer to this object.arrow_forward
- Y Differentiate the function below with respect to x. y = x² In (7x) =arrow_forwardB. - sinx+ C C. cscx+C D. cotx+C 5. Which of the following is NOT true? A The notation we use for the antiderivative of a function f(x) is S f(x) dx B. The antiderivative of a function f(x) is equal to the derivative of the function f(x). C. If f(x) is the derivative of F(x), then S f(x) dx = F(x) + C, where Cis some %3D constant. D. If f(x) is the derivative of F(x), then F(x) + C, where C is some constant is the antiderivative of f (x).arrow_forward1:48 O O 25.0 :4G KB/S 99 docs.google.com/forms/ 71 Which is the dx of the equation y = e 2x +3? O 2 B. x+ 3 C. 2x + 3 X + 3 O 2X + 3 2e 2x+3 Option 4 It is referred as the value of f(x) if xo is in the domain of f(x) and f(xo)2 f(x)for all values of x in the domain of f(x). Absolute maximum value X, +arrow_forward
- of = yexy – 8xy +2? Select all that apply. dx For which functions does Select one or more: a. f (x, y) = e*y – 4x²y + 2x + 4 - b. f(x, y) = e*y – 8x - c.f(x, y) = xye*y – 4x²y + 4y С. d.f(x, y) 3 е*у — 8ху + 2у %3D e. f(x, y) = e*y – 4x²y + 2xarrow_forward| (Zero temparature ends ) Suppose that a copper rod of lenght 50 cm was placed into a reservoir with hot water at 50° C so that half of it is in the air at 20°C. At t=0 , the rod is taken out and its ends are kept at constant ambient temparature of 20° c. Let us denote the difference between the rod's temparature and the ambient temparature by U(x,t) , where x is the distance from the left end of the rod , x=0. The U(x,t) is a solution of the initial boundary value problem: U t = x U xx = 1.14 With boundary conditions as U (0,t ) = U(50,t ) = 0 (30, 0 < x < 25 0, 25 < x < 50 Initial condition : U(x,0) = Find the solution U(x,t) of the given problem.arrow_forwardFor each statement, decide whether it is TRUE or FALSE. • A function f can have two different antiderivatives. [ Select ] • A function F can be an antiderivative of two different functions. [ Select ] • There is only one function y= f(x) satisfying the following Initial Value Problem: dy .2 = x + cos x dx y(0) = 5 . [ Select ]arrow_forward
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