   Chapter 8.3, Problem 62E

Chapter
Section
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: 0π3sec32xtanxdx

Formula used:

undu=un+1n+1+c

Calculation:

Consider the integral,

0π3sec32xtanxdx

Rewrite as an integral,

0π3sec32xtanxdx=0π3sec12xsecxtanxdx

Substitute,

u=secxdu=secxtanxdx

Therefore,

0π3sec32xtanxdx=0π3u12</

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