   Chapter 8.3, Problem 67E

Chapter
Section
Textbook Problem

# Comparing Methods Find the indefinite integral ∫ sec x cos x   d x using the given method. Explain how your answers differ for each method.(a) Substitution when u = sin x (b) Substitution where u = cos x (c) Integration by parts(d) Using the identity sin 2 x = 2 sin x cos x

(a)

To determine

To calculate:

The following indefinite integralusing substituting method, sinxcosxdx

Explanation

Given:

The given expression is sinxcosxdx,

Substitute u=sinx

Formula used:

Calculation:

Consider following indefinite integral,

sinxcosxdx

As given we have to evaluate sinxcosxdx using substitution method.

u=sinxdu=cosxdxsinxcosxdx=

(b)

To determine

To calculate:

The following indefinite integral sinxcosxdx

(c)

To determine

To calculate:

The following indefinite integral sinxcosxdx

(d)

To determine

To calculate:

The following indefinite integral sinxcosxdx

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