Chapter 5: Q. 12 (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 dx is .
Chapter 5: Q. 12 (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 dx is .
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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.
Domains and ranges of inverse trigonometric functions: For each function that follows, (a) list the domain and range, (b) sketch a labeled graph, and (c) discuss the domains and ranges in the context of the unit circle.
Solve the integral:
Examples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.
(a) An integral with which we could reasonably apply trigonometric substitution with .
(b) An integral with which we could reasonably apply trigonometric substitution with .
(c) An integral with which we could reasonably apply trigonometric substitution with .
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