   Chapter 8.3, Problem 7E

Chapter
Section
Textbook Problem

# Finding an Indefinite Integral Involving Sine and Cosine In Exercises 3-14, find the indefinite integral. ∫ sin 3 2 θ cos 2 θ   d θ

To determine

To calculate: Indefinite integral of the expression.

Explanation

Given: The expression sin32θcos2θdθ.

Calculation:

Indefinite integral of a function states that the function is integrated without any limits, and if limits are applied, they can be done so directly by putting the limits into the integrated expression.

Consider the integral to be I,

I=sin32θcos2θdθ (I)

Simplify it to a form, such that we can use power rule,

I=sin32θcos2θdθI=(sin22θ)sin2θcos2θdθI=(1cos22θ)(cos2θ)12sin2θdθI=(cos2θ)12sin2θdθ(cos2θ)52sin2θdθ

For the integral involving power of sine and cosine, let us use power rule to get,

u=cos2θdu=sin

### 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

#### Find more solutions based on key concepts 