 5.9.1: Assume that g is continuous on [a, b] and that f is continuouson an...
 5.9.2: In each part, use the substitution to replace the given integralwit...
 5.9.3: Evaluate the integral by making an appropriate substitution.(a) 0si...
 5.9.4: 14 Express the integral in terms of the variable u, but do not eval...
 5.9.5: 518 Evaluate the definite integral two ways: first by a usubstituti...
 5.9.6: 518 Evaluate the definite integral two ways: first by a usubstituti...
 5.9.7: 518 Evaluate the definite integral two ways: first by a usubstituti...
 5.9.8: 518 Evaluate the definite integral two ways: first by a usubstituti...
 5.9.9: 518 Evaluate the definite integral two ways: first by a usubstituti...
 5.9.10: 518 Evaluate the definite integral two ways: first by a usubstituti...
 5.9.11: 518 Evaluate the definite integral two ways: first by a usubstituti...
 5.9.12: 518 Evaluate the definite integral two ways: first by a usubstituti...
 5.9.13: 518 Evaluate the definite integral two ways: first by a usubstituti...
 5.9.14: 518 Evaluate the definite integral two ways: first by a usubstituti...
 5.9.15: 518 Evaluate the definite integral two ways: first by a usubstituti...
 5.9.16: 518 Evaluate the definite integral two ways: first by a usubstituti...
 5.9.17: 518 Evaluate the definite integral two ways: first by a usubstituti...
 5.9.18: 518 Evaluate the definite integral two ways: first by a usubstituti...
 5.9.19: 1922 Evaluate the definite integral by expressing it in termsof u a...
 5.9.20: 1922 Evaluate the definite integral by expressing it in termsof u a...
 5.9.21: 1922 Evaluate the definite integral by expressing it in termsof u a...
 5.9.22: 1922 Evaluate the definite integral by expressing it in termsof u a...
 5.9.23: A particle moves with a velocity of v(t) = sin t m/s alongan saxis...
 5.9.24: A particle moves with a velocity of v(t) = 3 cos 2t m/salong an sa...
 5.9.25: Find the area under the curve y = 9/(x + 2)2 over the interval[1, 1].
 5.9.26: Find the area under the curve y = 1/(3x + 1)2 over the interval[0, 1].
 5.9.27: Find the area of the region enclosed by the graphs ofy = 1/1 9x2, y...
 5.9.28: Find the area of the region enclosed by the graphs ofy = sin1 x, x ...
 5.9.29: Find the average value of f (x) = x/(5x2 + 1)2 over theinterval [0,...
 5.9.30: Find the average value of f (x) = e3x /(1 + e6x ) over theinterval ...
 5.9.31: 3150 Evaluate the integrals by any method. 51dx2x 1
 5.9.32: 3150 Evaluate the integrals by any method. 215x 1 dx
 5.9.33: 3150 Evaluate the integrals by any method. 11x2 dxx3 + 9
 5.9.34: 3150 Evaluate the integrals by any method. /26 sin x(cos x + 1)5 dx
 5.9.35: 3150 Evaluate the integrals by any method. 31x + 2x2 + 4x + 7dx
 5.9.36: 3150 Evaluate the integrals by any method. 21dxx2 6x + 9
 5.9.37: 3150 Evaluate the integrals by any method. /404 sin x cos x dx
 5.9.38: 3150 Evaluate the integrals by any method. /40tan x sec2 x dx
 5.9.39: 3150 Evaluate the integrals by any method. 05x cos(x2)dx
 5.9.40: 3150 Evaluate the integrals by any method. 4221x sin x dx
 5.9.41: 3150 Evaluate the integrals by any method. /9/12sec2 3 d
 5.9.42: 3150 Evaluate the integrals by any method. /60tan 2 d
 5.9.43: 3150 Evaluate the integrals by any method. 10y2 dy4 3y
 5.9.44: 3150 Evaluate the integrals by any method. 41x dx5 + x
 5.9.45: 3150 Evaluate the integrals by any method. e0dx2x + e
 5.9.46: 3150 Evaluate the integrals by any method. 21xex2dx
 5.9.47: 3150 Evaluate the integrals by any method. 10x 4 3x4dx
 5.9.48: 3150 Evaluate the integrals by any method. 211x4 x dx
 5.9.49: 3150 Evaluate the integrals by any method. 1/3011 + 9x2 dx
 5.9.50: 3150 Evaluate the integrals by any method. 21x3 + x4 dx
 5.9.51: (a) Use a CAS to find the exact value of the integral /60sin4 x cos...
 5.9.52: (a) Use a CAS to find the exact value of the integral /4/4tan4 x dx...
 5.9.53: (a) Find 10f(3x + 1)dx if 41f(x) dx = 5.(b) Find 30f(3x) dx if 90f(...
 5.9.54: Given that m and n are positive integers, show that 10xm(1 x)n dx =...
 5.9.55: Given that n is a positive integer, show that /20sinn x dx = /20cos...
 5.9.56: Given that n is a positive integer, evaluate the integral 10x(1 x)n dx
 5.9.57: 5760 Medication can be administered to a patient in differentways. ...
 5.9.58: 5760 Medication can be administered to a patient in differentways. ...
 5.9.59: 5760 Medication can be administered to a patient in differentways. ...
 5.9.60: 5760 Medication can be administered to a patient in differentways. ...
 5.9.61: Suppose that at time t = 0 there are 750 bacteria in a growthmedium...
 5.9.62: Suppose that a particle moving along a coordinate line hasvelocity ...
 5.9.63: (a) The accompanying table shows the fraction of the Moonthat is il...
 5.9.64: Electricity is supplied to homes in the form of alternatingcurrent,...
 5.9.65: Find a positive value of k such that the area under the graphof y =...
 5.9.66: Use a graphing utility to estimate the value of k (k > 0) sothat th...
 5.9.67: (a) Find the limitlimn+nk=1sin(k/n)nby evaluating an appropriate de...
 5.9.68: LetI = 1111 + x2 dx(a) Explain why I > 0.(b) Show that the substitu...
 5.9.69: (a) Prove that if f is an odd function, then aaf(x) dx = 0and give ...
 5.9.70: Show that if f and g are continuous functions, then t0f(t x)g(x) dx...
 5.9.71: (a) LetI = a0f(x)f(x) + f(a x)dxShow that I = a/2.[Hint: Let u = a ...
 5.9.72: Evaluate(a) 11xcos(x2)dx(b) 0sin8 x cos5 x dx.[Hint: Use the substi...
 5.9.73: Writing The two substitution methods discussed in thissection yield...
 5.9.74: Writing In some cases, the second method for the evaluationof defin...
Solutions for Chapter 5.9: EVALUATING DEFINITE INTEGRALS BY SUBSTITUTION
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 5.9: EVALUATING DEFINITE INTEGRALS BY SUBSTITUTION
Get Full SolutionsCalculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. Since 74 problems in chapter 5.9: EVALUATING DEFINITE INTEGRALS BY SUBSTITUTION have been answered, more than 38325 students have viewed full stepbystep solutions from this chapter. Chapter 5.9: EVALUATING DEFINITE INTEGRALS BY SUBSTITUTION includes 74 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Coefficient
The real number multiplied by the variable(s) in a polynomial term

Coefficient matrix
A matrix whose elements are the coefficients in a system of linear equations

Combinatorics
A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined

De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

Decreasing on an interval
A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

Leading coefficient
See Polynomial function in x

Logarithmic regression
See Natural logarithmic regression

Mean (of a set of data)
The sum of all the data divided by the total number of items

Natural logarithm
A logarithm with base e.

nth root
See Principal nth root

Octants
The eight regions of space determined by the coordinate planes.

Rational numbers
Numbers that can be written as a/b, where a and b are integers, and b ? 0.

Solve a system
To find all solutions of a system.

Solve by substitution
Method for solving systems of linear equations.

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Sum of an infinite series
See Convergence of a series

Summation notation
The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series

Vertical asymptote
The line x = a is a vertical asymptote of the graph of the function ƒ if limx:a+ ƒ1x2 = q or lim x:a ƒ1x2 = q.

Vertical translation
A shift of a graph up or down.

Weights
See Weighted mean.