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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.4 - Problem 76e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.4 - Problem 76e

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# Rational functions of trigonometric functions | Ch 7.4 - 76E

ISBN: 9780321570567 2

## Solution for problem 76E Chapter 7.4

Calculus: Early Transcendentals | 1st Edition

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Problem 76E

Problem 76E

Rational functions of trigonometric functions

An integrand with trigonometric functions in the numerator and denominator can often be converted to a rational integrand using the substitution u =tan (x/2) or x = 2 tan−1 u. The following relations are used in making this change of variables.

A:

B:

C:

Evaluate .

Step-by-Step Solution:

Problem 76E

Rational functions of trigonometric functions
An integrand with trigonometric functions in the numerator and denominator can often be converted to a rational integrand using the substitution or
The following relations are used in making this change of variables:
A:

B:

C:

Evaluate
Solution:-
Step 1

(Making the indicated substitutions in the integral)
=

=

=

=

=
Since
, the integral now becomes,

Thus, the value of the integral  is

Step 2 of 1

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