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 20E
To determine

To find: The limit as a defined integral on the given interval

Expert Solution

Answer to Problem 20E

Defined integral on the interval [0,2]=02[43(x)2+6(x)5]dx

Explanation of Solution

Given information:

  limni=1n[43(xi)2+6(xi)5]Δx,[0,2]

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:

Comparing the given limit limni=1n[43(xi)2+6(xi)5]Δx

with

  abf(x)dx=limni=1nf(xi)Δx

Here f(x)=[43(x)2+6(x)5]

And a=0

And

  b=2

Substitute a=0 and b=2

And f(x)=[43(x)2+6(x)5]

So, define integral on the interval [0,2]=02[43(x)2+6(x)5]dx

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