   Chapter 5.1, Problem 17E

Chapter
Section
Textbook Problem

# Sketch the region enclosed by the given curves and find its area. x = 2 y 2 ,   x = 4 + y 2

To determine

To:

Sketch the region and find the enclosed area

Explanation

1) Concept:

Formula:

The area A of the region bounded by the curves x=f(y), x=g(y) and the lines y=c and y=d  is

A= cdfy-gydy

Let’s denote the right boundary curve by xR and the left boundary by xL, then the area between these curves is given by

A=cdxR-xLdy

2) Given:

x=2y2 and   x=4+y2

3) Calculation:

The point of intersection occurs when both equations are equal to each other, that is,

2y2=4+y2

y2=4

Thus, the points of intersection are at y=-2 and   y=2. The region is sketched in the following figure.

Here, the right curve is x=4+y2 and the left curve is x=2y2. Therefore,

xR=4+y2

### 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

#### Simplify Simplify the rational expression. 18. x2x2x21

Precalculus: Mathematics for Calculus (Standalone Book)

#### Evaluate the expression sin Exercises 116. (2)3

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Rewritten in reverse order,

Study Guide for Stewart's Multivariable Calculus, 8th 