Chapter 8.3, Problem 62E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Evaluating a Definite Integral In Exercises 59–66, evaluate the definite integral. ∫ 0 π / 3 sec 3 / 2   x   tan   x   d x

To determine

To calculate: The definite integral 0π3sec32xtanxdx.

Explanation

Given: âˆ«0Ï€3sec32xtanxdx

Formula used:

âˆ«undu=un+1n+1+c

Calculation:

Consider the integral,

âˆ«0Ï€3sec32xtanxdx

Rewrite as an integral,

âˆ«0Ï€3sec32xtanxdx=âˆ«0Ï€3sec12xsecxtanxdx

Substitute,

u=secxdu=secxtanxdx

Therefore,

âˆ«0Ï€3sec32xtanxdx=âˆ«0Ï€3u12</

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