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 21E
To determine

To Find: The integral of 15(1+3x)dx

Expert Solution

Answer to Problem 21E

The integral of 15(1+3x)dx=42

Explanation of Solution

Given information:

  15(1+3x)dx

Concept Used:

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

  abf(x)dx=limni=1nf(xi)Δx

Calculation:

The integral is obtained as:

  15(1+3x)dxΔx=banΔx=5+1nΔx=6nxi=a+iΔxxi=1+6inf(xi)=(1+3(1+6in))

And

  Δx=6n

  limni=1nf(xi)Δx

  limni=1n(1+3(1+6in))6n

  limn(2n+18n×n(n+1)2)6n

  limn(12+54(1+1n))=42

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