Chapter 5: Q.10 (page 477)
Draw pictures to illustrate why the comparison test for improper integrals makes intuitive sense for both convergence comparisons and for divergence comparisons.
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Find three integrals in Exercises 39–74 that can be solved without using trigonometric substitution.
Solve the integralthree ways:
(a) with the substitution followed by back substitution;
(b) with integration by parts, choosing localid="1648814744993"
(c) with the trigonometric substitution x = sec u.
Complete the square for each quadratic in Exercises 28–33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.
Solve each of the integrals in Exercises 39–74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
Solve given definite integral.
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