Chapter 5: Q 27. (page 429)
Solve the integral:
Short Answer
The required answer is.
Chapter 5: Q 27. (page 429)
Solve the integral:
The required answer is.
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Get started for freeExplain how to know when to use the trigonometric substitutions , Describe the trigonometric identity and the triangle that will be needed in each case. What are the possible values for and in each case?
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.
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 .
For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
Solve the following two ways:
(a) with the trigonometric substitution x = 3 tan u;
(b) with algebra and the derivative of the arctangent.
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