The integral of ∫ 0 5 ( 1 + 2 x 3 ) 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 24E
To determine

To Find: The integral of ∫05(1+2x3)dx

Expert Solution

The integral of 05(1+2x3)dx=6352

Explanation of Solution

Given information:

05(1+2x3)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:

05(1+2x3)dxΔx=banΔx=50nΔx=5nxi=a+iΔxxi=5inf(xi)=1+2(5in)3

And

Δx=5nlimni=1nf(xi)Δxlimni=1n(1+2(5in)3)5nlimn(5+12504×n2(1+n)2n4)limn(5+12504×(1+1n)21)limn(5+12504×(1+1n)21)=6352

Hence,

The integral of 05(1+2x3)dx=6352

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