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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For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
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 the following two ways:
(a) with the substitution
(b) by completing the square and then applying the trigonometric substitution x + 2 = 2 sec u.
Solve given definite integrals.
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.
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