# The integral of ∫ 1 4 ( x 2 + 2 x − 5 ) d x

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 5.2, Problem 22E
To determine

## To Find: The integral of ∫14(x2+2x−5)dx

Expert Solution

The integral of 14(x2+2x5)dx=21

### Explanation of Solution

Given information:

14(x2+2x5)dx

Concept Used:

If f(x) is integrableon [a,b] , then

abf(x)dx=limni=1nf(xi)Δx

Where Δx=ban and xi=a+iΔx

Calculation:

The integral is obtained as:

14(x2+2x5)dxΔx=banΔx=41nΔx=3nxi=a+iΔxxi=1+3inf(xi)=(1+3in)2+2(1+3in)5

And

Δx=3nlimni=1nf(xi)Δxlimni=1n((1+3in)2+2(1+3in)5)3nlimn[3n×14n2+21n+32n]limn[42n2+63n+92n2]=21

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