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Chapter 5: Q 23. (page 495)
Defining improper integrals: Fill in the blanks, using limits and proper definite integrals to express each of the following types of improper integrals.
If f is continuous on [a, c) 鈭� (c, b] but not at x = c, then
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Give an example of an integral for which trigonometric substitution is possible but an easier method is available. Then give an example of an integral that we still don鈥檛 know how to solve given the techniques we know at this point.
Solve each of the integrals in Exercises 39鈥�74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
Solve the following two ways:
(a) with the trigonometric substitution x = 3 tan u;
(b) with algebra and the derivative of the arctangent.
Solve the integral:
List some things which would suggest that a certain substitution u(x) could be a useful choice. What do you look for when choosing u(x)?
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