Chapter 5: Q. 11 (page 417)
For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
Short Answer
The differential du in terms of the differential dxis .
Chapter 5: Q. 11 (page 417)
For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
The differential du in terms of the differential dxis .
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Get started for freeExplain why, if , then . Your explanation should include a discussion of domains and absolute values.
Suppose . Calculate and compare the values of the following definite integrals:
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Solvethe following two ways:
(a) with the substitution
(b) with the trigonometric substitution x = 2 tan u.
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.
Consider the integral from the reading at the beginning of the section.
(a) Use the inverse trigonometric substitution to solve this integral.
(b) Use the trigonometric substitution to solve the integral.
(c) Compare and contrast the two methods used in parts (a) and (b).
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