   Chapter 8.7, Problem 8E

Chapter
Section
Textbook Problem

Integration by Tables In Exercises 7-10, use a table of integrals with forms involving the trigonometric functions to find the indefinite integral. ∫ sin 4 x x   d x

To determine

To calculate: The value of the given indefinite integral sin4xxdx using the table of integrals.

Explanation

Given: We are given with the Indefinite integral expression sin4xxdx.

Formula used:

We will use Formula 48 and formula 50 from the table of integrals:

sin2udu=12(usinucosu)+c

sinnudu=sinn1ucosun+n1nsinn2udu

Calculation:

Compare the form of given Indefinite Integral with Formula 50 involving trigonometric functions:

sinnudu=sinn1ucosun+n1nsinn2udu

We assume that n=4 and u=x. Then du=12xdx, and thus we get that:

sin4xxdx=2sin4udu=2[sin41ucosu4+414sin42udu]=2[sin3ucosu4+34sin2udu]

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

Evaluate the integral. 11t(1t)2dt

Single Variable Calculus: Early Transcendentals, Volume I

Draw a polygon for the distribution of scores shown in the following table. X f 6 2 5 5 4 3 3 2 2 1

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

In problems 31-36, simplify each expression. 34.

Mathematical Applications for the Management, Life, and Social Sciences

Find f in terms of f and g. h(x) = f(g(sin 4x))

Single Variable Calculus: Early Transcendentals 