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

Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative. (take C = 0 ).

x ( x 2 1 ) 3 d x

To determine

To evaluate:

The given indefinite integral xx2-13dx.

Explanation

1) Concept:

i) The substitution rule

If u=g(x) is a differentiable function whose range is I and f is continuous on I, then f(gx)g'xdx=f(u)du. ii) Indefinite integral

xn dx=xn+1n+1+C  n-1

iii)

abcfxdx=cabfxdx

2) Given:

xx2-13dx

3) Calculation:

The given integral is xx2-13dx

Here, use the substitution method.

Substitute x2-1=u.

Differentiating with respect to x.

 2xdx=du

xdx=du2

Therefore, the given integral becomes

xx2-13dx=u3du2

=12u3du

Using concept ii),

=12u3+13+1+C

=12u44+C

=

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-4.1 P-11ESect-4.1 P-12ESect-4.1 P-13ESect-4.1 P-14ESect-4.1 P-15ESect-4.1 P-16ESect-4.1 P-17ESect-4.1 P-18ESect-4.1 P-19ESect-4.1 P-20ESect-4.1 P-21ESect-4.1 P-22ESect-4.1 P-23ESect-4.1 P-24ESect-4.1 P-25ESect-4.1 P-26ESect-4.1 P-27ESect-4.1 P-28ESect-4.1 P-29ESect-4.1 P-30ESect-4.1 P-31ESect-4.1 P-32ESect-4.2 P-1ESect-4.2 P-2ESect-4.2 P-3ESect-4.2 P-4ESect-4.2 P-5ESect-4.2 P-6ESect-4.2 P-7ESect-4.2 P-8ESect-4.2 P-9ESect-4.2 P-10ESect-4.2 P-11ESect-4.2 P-12ESect-4.2 P-13ESect-4.2 P-14ESect-4.2 P-15ESect-4.2 P-16ESect-4.2 P-17ESect-4.2 P-18ESect-4.2 P-19ESect-4.2 P-20ESect-4.2 P-21ESect-4.2 P-22ESect-4.2 P-23ESect-4.2 P-24ESect-4.2 P-25ESect-4.2 P-26ESect-4.2 P-27ESect-4.2 P-28ESect-4.2 P-29ESect-4.2 P-30ESect-4.2 P-31ESect-4.2 P-32ESect-4.2 P-33ESect-4.2 P-34ESect-4.2 P-35ESect-4.2 P-36ESect-4.2 P-37ESect-4.2 P-38ESect-4.2 P-39ESect-4.2 P-40ESect-4.2 P-41ESect-4.2 P-42ESect-4.2 P-43ESect-4.2 P-44ESect-4.2 P-45ESect-4.2 P-46ESect-4.2 P-47ESect-4.2 P-48ESect-4.2 P-49ESect-4.2 P-50ESect-4.2 P-51ESect-4.2 P-52ESect-4.2 P-53ESect-4.2 P-54ESect-4.2 P-55ESect-4.2 P-56ESect-4.2 P-57ESect-4.2 P-58ESect-4.2 P-59ESect-4.2 P-60ESect-4.2 P-61ESect-4.2 P-62ESect-4.2 P-63ESect-4.2 P-64ESect-4.2 P-65ESect-4.2 P-66ESect-4.2 P-67ESect-4.2 P-68ESect-4.2 P-69ESect-4.2 P-70ESect-4.2 P-71ESect-4.2 P-72ESect-4.2 P-73ESect-4.2 P-74ESect-4.2 P-75ESect-4.3 P-1ESect-4.3 P-2ESect-4.3 P-3ESect-4.3 P-4ESect-4.3 P-5ESect-4.3 P-6ESect-4.3 P-7ESect-4.3 P-8ESect-4.3 P-9ESect-4.3 P-10ESect-4.3 P-11ESect-4.3 P-12ESect-4.3 P-13ESect-4.3 P-14ESect-4.3 P-15ESect-4.3 P-16ESect-4.3 P-17ESect-4.3 P-18ESect-4.3 P-19ESect-4.3 P-20ESect-4.3 P-21ESect-4.3 P-22ESect-4.3 P-23ESect-4.3 P-24ESect-4.3 P-25ESect-4.3 P-26ESect-4.3 P-27ESect-4.3 P-28ESect-4.3 P-29ESect-4.3 P-30ESect-4.3 P-31ESect-4.3 P-32ESect-4.3 P-33ESect-4.3 P-34ESect-4.3 P-35ESect-4.3 P-36ESect-4.3 P-37ESect-4.3 P-38ESect-4.3 P-39ESect-4.3 P-40ESect-4.3 P-41ESect-4.3 P-42ESect-4.3 P-43ESect-4.3 P-44ESect-4.3 P-45ESect-4.3 P-46ESect-4.3 P-47ESect-4.3 P-48ESect-4.3 P-49ESect-4.3 P-50ESect-4.3 P-51ESect-4.3 P-52ESect-4.3 P-53ESect-4.3 P-54ESect-4.3 P-55ESect-4.3 P-56ESect-4.3 P-57ESect-4.3 P-58ESect-4.3 P-59ESect-4.3 P-60ESect-4.3 P-61ESect-4.3 P-62ESect-4.3 P-63ESect-4.3 P-64ESect-4.3 P-65ESect-4.3 P-66ESect-4.3 P-67ESect-4.3 P-68ESect-4.3 P-69ESect-4.3 P-70ESect-4.3 P-71ESect-4.3 P-72ESect-4.3 P-73ESect-4.3 P-74ESect-4.3 P-75ESect-4.3 P-76ESect-4.3 P-77ESect-4.3 P-78ESect-4.3 P-79ESect-4.3 P-80ESect-4.3 P-81ESect-4.3 P-82ESect-4.3 P-83ESect-4.3 P-84ESect-4.4 P-1ESect-4.4 P-2ESect-4.4 P-3ESect-4.4 P-4ESect-4.4 P-5ESect-4.4 P-6ESect-4.4 P-7ESect-4.4 P-8ESect-4.4 P-9ESect-4.4 P-10ESect-4.4 P-11ESect-4.4 P-12ESect-4.4 P-13ESect-4.4 P-14ESect-4.4 P-15ESect-4.4 P-16ESect-4.4 P-17ESect-4.4 P-18ESect-4.4 P-19ESect-4.4 P-20ESect-4.4 P-21ESect-4.4 P-22ESect-4.4 P-23ESect-4.4 P-24ESect-4.4 P-25ESect-4.4 P-26ESect-4.4 P-27ESect-4.4 P-28ESect-4.4 P-29ESect-4.4 P-30ESect-4.4 P-31ESect-4.4 P-32ESect-4.4 P-33ESect-4.4 P-34ESect-4.4 P-35ESect-4.4 P-36ESect-4.4 P-37ESect-4.4 P-38ESect-4.4 P-39ESect-4.4 P-40ESect-4.4 P-41ESect-4.4 P-42ESect-4.4 P-43ESect-4.4 P-44ESect-4.4 P-45ESect-4.4 P-46ESect-4.4 P-47ESect-4.4 P-48ESect-4.4 P-49ESect-4.4 P-50ESect-4.4 P-51ESect-4.4 P-52ESect-4.4 P-53ESect-4.4 P-54ESect-4.4 P-55ESect-4.4 P-56ESect-4.4 P-57ESect-4.4 P-58ESect-4.4 P-59ESect-4.4 P-60ESect-4.4 P-61ESect-4.4 P-62ESect-4.4 P-63ESect-4.4 P-64ESect-4.4 P-65ESect-4.4 P-66ESect-4.4 P-67ESect-4.4 P-68ESect-4.4 P-69ESect-4.4 P-70ESect-4.4 P-71ESect-4.4 P-72ESect-4.4 P-73ESect-4.4 P-74ESect-4.5 P-1ESect-4.5 P-2ESect-4.5 P-3ESect-4.5 P-4ESect-4.5 P-5ESect-4.5 P-6ESect-4.5 P-7ESect-4.5 P-8ESect-4.5 P-9ESect-4.5 P-10ESect-4.5 P-11ESect-4.5 P-12ESect-4.5 P-13ESect-4.5 P-14ESect-4.5 P-15ESect-4.5 P-16ESect-4.5 P-17ESect-4.5 P-18ESect-4.5 P-19ESect-4.5 P-20ESect-4.5 P-21ESect-4.5 P-22ESect-4.5 P-23ESect-4.5 P-24ESect-4.5 P-25ESect-4.5 P-26ESect-4.5 P-27ESect-4.5 P-28ESect-4.5 P-29ESect-4.5 P-30ESect-4.5 P-31ESect-4.5 P-32ESect-4.5 P-33ESect-4.5 P-34ESect-4.5 P-35ESect-4.5 P-36ESect-4.5 P-37ESect-4.5 P-38ESect-4.5 P-39ESect-4.5 P-40ESect-4.5 P-41ESect-4.5 P-42ESect-4.5 P-43ESect-4.5 P-44ESect-4.5 P-45ESect-4.5 P-46ESect-4.5 P-47ESect-4.5 P-48ESect-4.5 P-49ESect-4.5 P-50ESect-4.5 P-51ESect-4.5 P-52ESect-4.5 P-53ESect-4.5 P-54ESect-4.5 P-55ESect-4.5 P-56ESect-4.5 P-57ESect-4.5 P-58ESect-4.5 P-59ESect-4.5 P-60ESect-4.5 P-61ESect-4.5 P-62ESect-4.5 P-63ESect-4.5 P-64ESect-4.5 P-65ESect-4.5 P-66ESect-4.5 P-67ESect-4.5 P-68ESect-4.5 P-69ESect-4.5 P-70ESect-4.5 P-71ESect-4.5 P-72ESect-4.5 P-73ESect-4.5 P-74ESect-4.5 P-75ESect-4.5 P-76ESect-4.5 P-77ESect-4.5 P-78ESect-4.5 P-79ESect-4.5 P-80ESect-4.5 P-81ESect-4.5 P-82ESect-4.5 P-83ESect-4.5 P-84ESect-4.5 P-85ESect-4.R P-1CCSect-4.R P-2CCSect-4.R P-3CCSect-4.R P-4CCSect-4.R P-5CCSect-4.R P-6CCSect-4.R P-7CCSect-4.R P-8CCSect-4.R P-9CCSect-4.R P-1TFQSect-4.R P-2TFQSect-4.R P-3TFQSect-4.R P-4TFQSect-4.R P-5TFQSect-4.R P-6TFQSect-4.R P-7TFQSect-4.R P-8TFQSect-4.R P-9TFQSect-4.R P-10TFQSect-4.R P-11TFQSect-4.R P-12TFQSect-4.R P-13TFQSect-4.R P-14TFQSect-4.R P-15TFQSect-4.R P-16TFQSect-4.R P-17TFQSect-4.R P-18TFQSect-4.R P-1ESect-4.R P-2ESect-4.R P-3ESect-4.R P-4ESect-4.R P-5ESect-4.R P-6ESect-4.R P-7ESect-4.R P-8ESect-4.R P-9ESect-4.R P-10ESect-4.R P-11ESect-4.R P-12ESect-4.R P-13ESect-4.R P-14ESect-4.R P-15ESect-4.R P-16ESect-4.R P-17ESect-4.R P-18ESect-4.R P-19ESect-4.R P-20ESect-4.R P-21ESect-4.R P-22ESect-4.R P-23ESect-4.R P-24ESect-4.R P-25ESect-4.R P-26ESect-4.R P-27ESect-4.R P-28ESect-4.R P-29ESect-4.R P-30ESect-4.R P-31ESect-4.R P-32ESect-4.R P-33ESect-4.R P-34ESect-4.R P-35ESect-4.R P-36ESect-4.R P-37ESect-4.R P-38ESect-4.R P-39ESect-4.R P-40ESect-4.R P-41ESect-4.R P-42ESect-4.R P-43ESect-4.R P-44ESect-4.R P-45ESect-4.R P-46ESect-4.R P-47ESect-4.R P-48ESect-4.R P-49ESect-4.R P-50ESect-4.R P-51ESect-4.R P-52ESect-4.R P-53ESect-4.R P-54ESect-4.R P-55ESect-4.R P-56ESect-4.R P-57ESect-4.R P-58ESect-4.P P-1PSect-4.P P-2PSect-4.P P-3PSect-4.P P-4PSect-4.P P-5PSect-4.P P-6PSect-4.P P-7PSect-4.P P-8PSect-4.P P-9PSect-4.P P-10PSect-4.P P-11PSect-4.P P-12PSect-4.P P-13PSect-4.P P-14PSect-4.P P-15PSect-4.P P-16PSect-4.P P-17PSect-4.P P-18P

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)

U.S. Airplane Passenger Projections A report issued by the U.S. Department of Transportation in 2012 predicted ...

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

Finding a Derivative In Exercises 47104, find the derivative of the function. h(x)=ln(2x2+3)

Calculus: Early Transcendental Functions (MindTap Course List)

The critical numbers of f(x) = 3x4 = 20x3 36x2 are: a) 0, 1, 6 b) 0, 1, 6 c) 0, 1, 6 d) 0, 1, 6

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

The normal plane to at t = 1 has equation:

Study Guide for Stewart's Multivariable Calculus, 8th

What is the novelty effect, and how does it affect a studys external validity?

Research Methods for the Behavioral Sciences (MindTap Course List)

Explain how the purpose of a correctional study differs from the purpose of an experimental study.

Research Methods for the Behavioral Sciences (MindTap Course List)

Write each expression using exponents. xxxyy

College Algebra (MindTap Course List)