   Chapter 7.2, Problem 18E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ sin x   cos ( 1 2 x )   d x

To determine

To evaluate: The trigonometric integral sinxcos(12x)dx

Explanation

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

Formula used:

When power of sine in the integral is odd, save one sine factor and use the identity sin2x=1cos2x to rewrite other terms in cosine function form:

sin2k+1xcosnxdx=cosnx(1cos2x)ksinxdx

Then, use the substitution u=cosx

Given:

The integral, sinxcos(12x)dx.

Calculation:

Rewrite the given integral by making the substitution u=12x, du=12dx:

sinxcos(12x)dx=sin(2u)cosu(2du)=2sin2ucosudu

Use the identity sin2u=2sinucosu:

2sin2ucosudu

### 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

#### In the figure, mEFG=68 and m3=33. Find m4.

Elementary Geometry For College Students, 7e

#### limx(lnx)1/x= a) 0 b) 1 c) e d)

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

#### The graph of is: a) b) c) d)

Study Guide for Stewart's Multivariable Calculus, 8th 