   Chapter 13, Problem 13RE ### 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 7-18. ∫ − 1 2 ( x 2 + x )   d x

To determine

To calculate: The value of the integral 12(x2+x)dx.

Explanation

Given Information:

The provided integral is, 12(x2+x)dx.

Formula used:

The definite integral of a function f on a closed interval [a,b] is, abf(x)dx=F(b)F(a).

The simple power rule of integrals, xndx=xn+1n+1+C.

The sum or difference rule of definite integral ab(f(x)±g(x))dx=abf(x)dx±abg(x)dx.

Calculation:

Consider the provided integral, 12(x2+x)dx.

Use the sum or difference rule of definite integral ab(f(x)±g(x))dx=abf(x)dx±abg(x)dx.

12(x2+x)dx=12x2dx+12xdx

Use the simple power rule of integrals, xndx=xn+1n+1+C

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