   Chapter 7.3, Problem 11E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 0 1 / 2 x 1 − 4 x 2   d x

To determine

To evaluate: The given integral 012x14x2dx.

Explanation

Integration involving terms of the form a2x2 can be simplified by using the trigonometric substitution x=asinθ. However, at times a simple algebraic substitution can also simplify the integral.

Formula used:

The derivative of xn is nxn1dx.

Given:

The integral, 012x14x2dx

Calculation:

Use the substitution t=14x2 to simplify the integral. the limits of the integral will change as:

x0, then t1x12, then t0

The derivative of t will be dt=8xdx, so the integral will be:

012x14x2dx=&

### 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 indefinite integral. eu(1eu)2du

Single Variable Calculus: Early Transcendentals, Volume I

#### In Exercises 516, evaluate the given quantity. log5125

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Name the graph of a quadratic function.

Mathematical Applications for the Management, Life, and Social Sciences

#### If y = f (g(x)) then y′ = f′(g′(x)).

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

#### The harmonic series is: 1 + 2 + 3 + 4 + …

Study Guide for Stewart's Multivariable Calculus, 8th 