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Rational functions of trigonometric functions | Ch 7.4 - 76E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 76E Chapter 7.4

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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

Chapter 7.4, Problem 76E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Rational functions of trigonometric functions | Ch 7.4 - 76E