   Chapter 12.1, Problem 27E ### 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. ∫ ( x 9 − 1 x 3 + 2 x 3 )   d x

To determine

To calculate: The integral (x91x3+2x3)dx.

Explanation

Given Information:

The provided integral is (x91x3+2x3)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:

(x91x3+2x3)dx

Use the property of integrals:

[u(x)±v(x)]dx=u(x)dx+v(x)dx

To rewrite the provided integral as:

(x91x3+2x3)dx=x9dxx3dx+2x1/3dx

Use the power rule of integrals:

xndx=xn+1n+1+C

And, the property of integrals:

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