   Chapter 12.2, Problem 19E ### Mathematical Applications for the ...

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

#### Solutions

Chapter
Section ### 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. ∫ 2 ( x 3 − 1 ) ( x 4 − 4 x + 3 ) − 5 d x

To determine

To calculate: The value of the integral 2(x31)(x44x+3)5dx and also check the solution by differentiation.

Explanation

Given Information:

The provided integral is 2(x31)(x44x+3)5dx.

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,

2(x31)(x44x+3)5dx

Rewrite the integral by multiplying and dividing by 2 as,

124(x31)(x44x+3)5dx

Consider the power rule of integrals,

undu=un+1n+1+C

Now, to use the power rule, the integrand should have the function u(x) and its derivative u(x) and n1.

Let, u=x44x+3 and n=5

Differentiate u=x44x+3 with respect to x and get,

du=(4x34)dx

Now, all required parts are present, so the integral is of the form,

124(x31)(x44x+3)5dx=12u5du=12(

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