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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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Section
BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

Evaluate the integrals in Problems 7-36. Check your results by differentiation.

( x 3 + 1 ) 2 ( 3 x   d x )

To determine

To calculate: The value of the integral (x3+1)23xdx and also check the solution by differentiation.

Explanation

Given Information:

The provided integral is (x3+1)23xdx.

Formula used:

According to the power formula of integrals, if u=u(x), then,

undu=un+1n+1+C

According to the power rule of derivative,

ddx(xn)=nxn1

Calculation:

Consider the provided integral,

(x3+1)23xdx

Now, let x3+1=u

Differentiate x3+1=u with respect to x and get,

3x2dx=du

Here, this substitution does not work.

Hence, this method fails.

Now, simplify the integrand algebraically as,

(x3+1)23xdx=(x6+2x3+1)3xdx=(3x7+6x4+3x)dx

Use the power rule of integrals,

undu=un+1n+1+C

Now, integrate the above expression with respect to x as,

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Chapter 12 Solutions

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Sect-12.1 P-9ESect-12.1 P-10ESect-12.1 P-11ESect-12.1 P-12ESect-12.1 P-13ESect-12.1 P-14ESect-12.1 P-15ESect-12.1 P-16ESect-12.1 P-17ESect-12.1 P-18ESect-12.1 P-19ESect-12.1 P-20ESect-12.1 P-21ESect-12.1 P-22ESect-12.1 P-23ESect-12.1 P-24ESect-12.1 P-25ESect-12.1 P-26ESect-12.1 P-27ESect-12.1 P-28ESect-12.1 P-29ESect-12.1 P-30ESect-12.1 P-31ESect-12.1 P-32ESect-12.1 P-33ESect-12.1 P-34ESect-12.1 P-35ESect-12.1 P-36ESect-12.1 P-37ESect-12.1 P-38ESect-12.1 P-39ESect-12.1 P-40ESect-12.1 P-41ESect-12.1 P-42ESect-12.1 P-43ESect-12.1 P-44ESect-12.1 P-45ESect-12.1 P-46ESect-12.1 P-47ESect-12.1 P-48ESect-12.1 P-49ESect-12.1 P-50ESect-12.1 P-51ESect-12.1 P-52ESect-12.1 P-53ESect-12.1 P-54ESect-12.1 P-55ESect-12.1 P-56ESect-12.2 P-1CPSect-12.2 P-2CPSect-12.2 P-3CPSect-12.2 P-4CPSect-12.2 P-1ESect-12.2 P-2ESect-12.2 P-3ESect-12.2 P-4ESect-12.2 P-5ESect-12.2 P-6ESect-12.2 P-7ESect-12.2 P-8ESect-12.2 P-9ESect-12.2 P-10ESect-12.2 P-11ESect-12.2 P-12ESect-12.2 P-13ESect-12.2 P-14ESect-12.2 P-15ESect-12.2 P-16ESect-12.2 P-17ESect-12.2 P-18ESect-12.2 P-19ESect-12.2 P-20ESect-12.2 P-21ESect-12.2 P-22ESect-12.2 P-23ESect-12.2 P-24ESect-12.2 P-25ESect-12.2 P-26ESect-12.2 P-27ESect-12.2 P-28ESect-12.2 P-29ESect-12.2 P-30ESect-12.2 P-31ESect-12.2 P-32ESect-12.2 P-33ESect-12.2 P-34ESect-12.2 P-35ESect-12.2 P-36ESect-12.2 P-37ESect-12.2 P-38ESect-12.2 P-39ESect-12.2 P-40ESect-12.2 P-41ESect-12.2 P-42ESect-12.2 P-43ESect-12.2 P-44ESect-12.2 P-45ESect-12.2 P-46ESect-12.2 P-47ESect-12.2 P-48ESect-12.2 P-49ESect-12.2 P-50ESect-12.2 P-51ESect-12.2 P-52ESect-12.2 P-53ESect-12.2 P-54ESect-12.3 P-1CPSect-12.3 P-2CPSect-12.3 P-3CPSect-12.3 P-1ESect-12.3 P-2ESect-12.3 P-3ESect-12.3 P-4ESect-12.3 P-5ESect-12.3 P-6ESect-12.3 P-7ESect-12.3 P-8ESect-12.3 P-9ESect-12.3 P-10ESect-12.3 P-11ESect-12.3 P-12ESect-12.3 P-13ESect-12.3 P-14ESect-12.3 P-15ESect-12.3 P-16ESect-12.3 P-17ESect-12.3 P-18ESect-12.3 P-19ESect-12.3 P-20ESect-12.3 P-21ESect-12.3 P-22ESect-12.3 P-23ESect-12.3 P-24ESect-12.3 P-25ESect-12.3 P-26ESect-12.3 P-27ESect-12.3 P-28ESect-12.3 P-29ESect-12.3 P-30ESect-12.3 P-31ESect-12.3 P-32ESect-12.3 P-33ESect-12.3 P-34ESect-12.3 P-35ESect-12.3 P-36ESect-12.3 P-37ESect-12.3 P-38ESect-12.3 P-39ESect-12.3 P-40ESect-12.3 P-41ESect-12.3 P-42ESect-12.3 P-43ESect-12.3 P-44ESect-12.3 P-45ESect-12.3 P-46ESect-12.3 P-47ESect-12.3 P-48ESect-12.3 P-49ESect-12.3 P-50ESect-12.3 P-56ESect-12.4 P-1CPSect-12.4 P-2CPSect-12.4 P-3CPSect-12.4 P-4CPSect-12.4 P-1ESect-12.4 P-2ESect-12.4 P-3ESect-12.4 P-4ESect-12.4 P-5ESect-12.4 P-6ESect-12.4 P-7ESect-12.4 P-8ESect-12.4 P-9ESect-12.4 P-10ESect-12.4 P-11ESect-12.4 P-12ESect-12.4 P-13ESect-12.4 P-14ESect-12.4 P-15ESect-12.4 P-16ESect-12.4 P-17ESect-12.4 P-18ESect-12.4 P-19ESect-12.4 P-20ESect-12.4 P-21ESect-12.4 P-23ESect-12.4 P-24ESect-12.4 P-26ESect-12.5 P-1CPSect-12.5 P-2CPSect-12.5 P-3CPSect-12.5 P-1ESect-12.5 P-2ESect-12.5 P-3ESect-12.5 P-4ESect-12.5 P-5ESect-12.5 P-6ESect-12.5 P-7ESect-12.5 P-8ESect-12.5 P-9ESect-12.5 P-10ESect-12.5 P-11ESect-12.5 P-12ESect-12.5 P-13ESect-12.5 P-14ESect-12.5 P-15ESect-12.5 P-16ESect-12.5 P-17ESect-12.5 P-18ESect-12.5 P-19ESect-12.5 P-20ESect-12.5 P-21ESect-12.5 P-22ESect-12.5 P-23ESect-12.5 P-24ESect-12.5 P-25ESect-12.5 P-26ESect-12.5 P-27ESect-12.5 P-28ESect-12.5 P-29ESect-12.5 P-30ESect-12.5 P-31ESect-12.5 P-32ESect-12.5 P-33ESect-12.5 P-34ESect-12.5 P-35ESect-12.5 P-36ESect-12.5 P-37ESect-12.5 P-38ESect-12.5 P-39ESect-12.5 P-40ESect-12.5 P-41ESect-12.5 P-42ESect-12.5 P-43ESect-12.5 P-44ESect-12.5 P-45ESect-12.5 P-46ESect-12.5 P-47ESect-12.5 P-48ESect-12.5 P-49ESect-12.5 P-50ESect-12.5 P-51ESect-12.5 P-52ESect-12.5 P-53ESect-12.5 P-54ESect-12.5 P-55ESect-12.5 P-56ESect-12.5 P-57ESect-12.5 P-58ECh-12 P-1RECh-12 P-2RECh-12 P-3RECh-12 P-4RECh-12 P-5RECh-12 P-6RECh-12 P-7RECh-12 P-8RECh-12 P-9RECh-12 P-10RECh-12 P-11RECh-12 P-12RECh-12 P-13RECh-12 P-14RECh-12 P-15RECh-12 P-16RECh-12 P-17RECh-12 P-18RECh-12 P-19RECh-12 P-20RECh-12 P-21RECh-12 P-22RECh-12 P-23RECh-12 P-24RECh-12 P-25RECh-12 P-26RECh-12 P-27RECh-12 P-28RECh-12 P-29RECh-12 P-30RECh-12 P-31RECh-12 P-32RECh-12 P-33RECh-12 P-34RECh-12 P-35RECh-12 P-36RECh-12 P-37RECh-12 P-38RECh-12 P-39RECh-12 P-40RECh-12 P-41RECh-12 P-42RECh-12 P-43RECh-12 P-44RECh-12 P-45RECh-12 P-46RECh-12 P-47RECh-12 P-48RECh-12 P-49RECh-12 P-1TCh-12 P-2TCh-12 P-3TCh-12 P-4TCh-12 P-5TCh-12 P-6TCh-12 P-7TCh-12 P-8TCh-12 P-9TCh-12 P-10TCh-12 P-11TCh-12 P-12TCh-12 P-13TCh-12 P-14TCh-12 P-15TCh-12 P-16TCh-12 P-17TCh-12 P-18TCh-12 P-19TCh-12 P-20TCh-12 P-21TCh-12 P-22T

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