   Chapter 12.1, Problem 28E ### 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 5-28. Check your answers by differentiating. ∫ ( 3 x 8 + 4 x 8 − 5 x 5 )   d x

To determine

To calculate: The integral (3x8+4x85x5)dx.

Explanation

Given Information:

The provided integral is (3x8+4x85x5)dx

Formula used:

The properties of integrals:

[u(x)±v(x)]dx=u(x)dx±v(x)dx.

The power formula of integrals:

xndx=xn+1n+1+C (forn1)

The power rule of differentiation:

ddx(xn)=nxn1

The properties of integrals:

dx=x+C

Calculation:

Consider the provided integral:

(3x8+4x85x5)dx

Use the property of integrals:

[u(x)±v(x)]dx=u(x)dx±v(x)dx

To rewrite the provided integral as:

(3x8+4x85x5)dx=3x8dx+4x8dx5x1/5dx

Use the power rule of integrals:

xndx=xn+1n+1+C

And, the property of integrals:

dx=x+C

To obtain the integral as:

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