BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Find the area of the region bounded by the given curves.

y = x ,    y = x 2 ,    x = 2

To determine

To find:

The area of the region bounded by the given curves.

Explanation

1) Concept:

The area A of the region bounded by the curves y=fx,  y=gx, and the lines x=a, x=b, where f and g are continuous and fxg(x) for all x in a, b, is

A= abfx-gxdx

2)  Given:

The region bounded by curves y=x,  y=x2, x=2

3) Calculation:

The given region is bounded by curves y=x,  y=x2, x=2. We plot the graph below

From the graph, the region is divided into two parts.

From x=0 to x=1, the upper boundary curve is y=x and the lower boundary curve is y=x2

From x=1 to x=2, the upper boundary curve is y=x2 and the lower boundary curve is y=x

Therefore, the area of the region bounded by the curves y=x,  y=x2, x=2 between x=0 to x=2 is given by

A= 01x-x2dx+12x2- xdx

= 01x12-x2dx+12x2-x12dx

By using fundamental theorem of calculus and power rule,

A=x3232-x3301+

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
Sect-5.1 P-11ESect-5.1 P-12ESect-5.1 P-13ESect-5.1 P-14ESect-5.1 P-15ESect-5.1 P-16ESect-5.1 P-17ESect-5.1 P-18ESect-5.1 P-19ESect-5.1 P-20ESect-5.1 P-21ESect-5.1 P-22ESect-5.1 P-23ESect-5.1 P-24ESect-5.1 P-25ESect-5.1 P-26ESect-5.1 P-27ESect-5.1 P-28ESect-5.1 P-29ESect-5.1 P-30ESect-5.1 P-31ESect-5.1 P-32ESect-5.1 P-33ESect-5.1 P-34ESect-5.1 P-35ESect-5.1 P-36ESect-5.1 P-37ESect-5.1 P-38ESect-5.1 P-39ESect-5.1 P-40ESect-5.1 P-41ESect-5.1 P-42ESect-5.1 P-43ESect-5.1 P-44ESect-5.1 P-45ESect-5.1 P-46ESect-5.1 P-47ESect-5.1 P-48ESect-5.1 P-49ESect-5.1 P-50ESect-5.1 P-51ESect-5.1 P-52ESect-5.1 P-53ESect-5.1 P-54ESect-5.1 P-55ESect-5.1 P-56ESect-5.1 P-57ESect-5.1 P-58ESect-5.1 P-59ESect-5.1 P-60ESect-5.1 P-61ESect-5.1 P-62ESect-5.1 P-63ESect-5.1 P-64ESect-5.2 P-1ESect-5.2 P-2ESect-5.2 P-3ESect-5.2 P-4ESect-5.2 P-5ESect-5.2 P-6ESect-5.2 P-7ESect-5.2 P-8ESect-5.2 P-9ESect-5.2 P-10ESect-5.2 P-11ESect-5.2 P-12ESect-5.2 P-13ESect-5.2 P-14ESect-5.2 P-15ESect-5.2 P-16ESect-5.2 P-17ESect-5.2 P-18ESect-5.2 P-19ESect-5.2 P-20ESect-5.2 P-21ESect-5.2 P-22ESect-5.2 P-23ESect-5.2 P-24ESect-5.2 P-25ESect-5.2 P-26ESect-5.2 P-27ESect-5.2 P-28ESect-5.2 P-29ESect-5.2 P-30ESect-5.2 P-31ESect-5.2 P-32ESect-5.2 P-33ESect-5.2 P-34ESect-5.2 P-35ESect-5.2 P-36ESect-5.2 P-37ESect-5.2 P-38ESect-5.2 P-39ESect-5.2 P-40ESect-5.2 P-41ESect-5.2 P-42ESect-5.2 P-43ESect-5.2 P-44ESect-5.2 P-45ESect-5.2 P-46ESect-5.2 P-47ESect-5.2 P-48ESect-5.2 P-49ESect-5.2 P-50ESect-5.2 P-51ESect-5.2 P-52ESect-5.2 P-53ESect-5.2 P-54ESect-5.2 P-55ESect-5.2 P-56ESect-5.2 P-57ESect-5.2 P-58ESect-5.2 P-59ESect-5.2 P-60ESect-5.2 P-61ESect-5.2 P-62ESect-5.2 P-63ESect-5.2 P-64ESect-5.2 P-65ESect-5.2 P-66ESect-5.2 P-67ESect-5.2 P-68ESect-5.2 P-69ESect-5.2 P-70ESect-5.2 P-71ESect-5.2 P-72ESect-5.3 P-1ESect-5.3 P-2ESect-5.3 P-3ESect-5.3 P-4ESect-5.3 P-5ESect-5.3 P-6ESect-5.3 P-7ESect-5.3 P-8ESect-5.3 P-9ESect-5.3 P-10ESect-5.3 P-11ESect-5.3 P-12ESect-5.3 P-13ESect-5.3 P-14ESect-5.3 P-15ESect-5.3 P-16ESect-5.3 P-17ESect-5.3 P-18ESect-5.3 P-19ESect-5.3 P-20ESect-5.3 P-21ESect-5.3 P-22ESect-5.3 P-23ESect-5.3 P-24ESect-5.3 P-25ESect-5.3 P-26ESect-5.3 P-27ESect-5.3 P-28ESect-5.3 P-29ESect-5.3 P-30ESect-5.3 P-31ESect-5.3 P-32ESect-5.3 P-33ESect-5.3 P-34ESect-5.3 P-35ESect-5.3 P-36ESect-5.3 P-37ESect-5.3 P-38ESect-5.3 P-39ESect-5.3 P-40ESect-5.3 P-41ESect-5.3 P-42ESect-5.3 P-43ESect-5.3 P-44ESect-5.3 P-45ESect-5.3 P-46ESect-5.3 P-47ESect-5.3 P-48ESect-5.4 P-1ESect-5.4 P-2ESect-5.4 P-3ESect-5.4 P-4ESect-5.4 P-5ESect-5.4 P-6ESect-5.4 P-7ESect-5.4 P-8ESect-5.4 P-9ESect-5.4 P-10ESect-5.4 P-11ESect-5.4 P-12ESect-5.4 P-13ESect-5.4 P-14ESect-5.4 P-15ESect-5.4 P-16ESect-5.4 P-17ESect-5.4 P-18ESect-5.4 P-19ESect-5.4 P-20ESect-5.4 P-21ESect-5.4 P-22ESect-5.4 P-23ESect-5.4 P-24ESect-5.4 P-25ESect-5.4 P-26ESect-5.4 P-27ESect-5.4 P-28ESect-5.4 P-29ESect-5.4 P-30ESect-5.4 P-31ESect-5.4 P-32ESect-5.4 P-33ESect-5.4 P-34ESect-5.5 P-1ESect-5.5 P-2ESect-5.5 P-3ESect-5.5 P-4ESect-5.5 P-5ESect-5.5 P-6ESect-5.5 P-7ESect-5.5 P-8ESect-5.5 P-9ESect-5.5 P-10ESect-5.5 P-11ESect-5.5 P-12ESect-5.5 P-13ESect-5.5 P-14ESect-5.5 P-15ESect-5.5 P-16ESect-5.5 P-17ESect-5.5 P-18ESect-5.5 P-19ESect-5.5 P-20ESect-5.5 P-21ESect-5.5 P-22ESect-5.5 P-23ESect-5.5 P-24ESect-5.R P-1CCSect-5.R P-2CCSect-5.R P-3CCSect-5.R P-4CCSect-5.R P-5CCSect-5.R P-6CCSect-5.R P-1ESect-5.R P-2ESect-5.R P-3ESect-5.R P-4ESect-5.R P-5ESect-5.R P-6ESect-5.R P-7ESect-5.R P-8ESect-5.R P-9ESect-5.R P-10ESect-5.R P-11ESect-5.R P-12ESect-5.R P-13ESect-5.R P-14ESect-5.R P-15ESect-5.R P-16ESect-5.R P-17ESect-5.R P-18ESect-5.R P-19ESect-5.R P-20ESect-5.R P-21ESect-5.R P-22ESect-5.R P-23ESect-5.R P-24ESect-5.R P-25ESect-5.R P-26ESect-5.R P-27ESect-5.R P-28ESect-5.R P-29ESect-5.R P-30ESect-5.R P-31ESect-5.R P-32ESect-5.R P-33ESect-5.R P-34ESect-5.P P-1PSect-5.P P-2PSect-5.P P-3PSect-5.P P-4PSect-5.P P-5PSect-5.P P-6PSect-5.P P-7PSect-5.P P-8PSect-5.P P-9PSect-5.P P-10PSect-5.P P-11PSect-5.P P-12PSect-5.P P-13PSect-5.P P-14PSect-5.P P-15P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

In Exercises 1728, use the logarithm identities to obtain the missing quantity.

Finite Mathematics and Applied Calculus (MindTap Course List)

Sketch the graph of the function f(x) = {2x3ifx2x+3ifx2 and evaluate limxa+ f(x), limxaf(x), and limxaf(x) at t...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

The graph of x = 2 + 3t, y = 4 − t is a: circle ellipse line parabola

Study Guide for Stewart's Multivariable Calculus, 8th

f(x)={2x+1ifx11xif1xsinxifx is continuous: a) for all x b) for all x except x = 1 c) for all x except x = d) f...

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

Describe the process of counterbalancing and the benefits of using it in a within-subjects design.

Research Methods for the Behavioral Sciences (MindTap Course List)