BuyFind

Single Variable Calculus: Concepts...

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

Single Variable Calculus: Concepts...

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

Solutions

Chapter 5.2, Problem 23E
To determine

To Find: The integral of 02(2x2)dx

Expert Solution

Answer to Problem 23E

The integral of 02(2x2)dx=43

Explanation of Solution

Given information:

  02(2x2)dx

Concept Used:

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

  abf(x)dx=limni=1nf(xi)Δx

Where Δx=ban and xi=a+iΔx

Calculation:

The integral is obtained as:

  02(2x2)dx

And,

  Δx=banΔx=20nΔx=2nxi=a+iΔxxi=2inf(xi)=2(2in)2

Therefore,

  Δx=2n

So,

  limni=1nf(xi)Δxlimn0n(2(2in)2)2nlimn(48n3×n(n+1)(2n+1)6)limn(48n3×n3(1+1n)(2+1n)6)=43

Hence,

The integral of 02(2x2)dx=43

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