   Chapter 7.2, Problem 26E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 0 π / 4 sec 6 θ   tan 6 θ   d θ

To determine

To evaluate: The trigonometric integral 0π4sec6θtan6θdθ

Explanation

Trigonometric integral of the form tanmxsecnxdx can be solved using strategies depending on whether m and n are odd or even.

Formula used:

When power of secant in the integral is even, save one sec2x factor and use the identity sec2x=1+tan2x to rewrite other terms in tangent function form:

tanmxsec2kxdx=tanmx(1+tan2x)k1sec2xdx

Then, use the substitution u=tanx

Given:

The integral, 0π4sec6θtan6θdθ.

Calculation:

Rewrite the given integral in terms of tangent, saving one sec2x term:

0π4sec6θtan6θdθ=0π4sec4θtan6θsec2θdθ=0π4(sec2θ)2tan6θsec2θdθ

Use the identity sec2x=1+tan2x

0π4(sec2θ)2tan6θsec2θdθ=0π4(1+tan2θ)2tan6θsec2θdθ

Use the substitution u=tanθ and du=sec2θdθ

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Factoring Factor the expression completely. 27. x4 2x2 + 1

Precalculus: Mathematics for Calculus (Standalone Book)

#### In Problems 15-22, evaluate each function as indicated.

Mathematical Applications for the Management, Life, and Social Sciences

#### Polar coordinates of the point with rectangular coordinates (5, 5) are: (25, 0)

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 