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 41E
To determine

To find: as a single integral in the form abf(x)dx

Expert Solution

Answer to Problem 41E

As a single integral in the form abf(x)dx of

  21f(x)dx+15f(x)dx21f(x)dx

  =15f(x)dx

Explanation of Solution

Given information:

The integral is:

  22f(x)dx+25f(x)dx21f(x)dx

Concept Used:

  abf(x)dx=acf(x)dx+cbf(x)dx

Calculation:

Use abf(x)dx=acf(x)dx+cbf(x)dx

  22f(x)dx+25f(x)dx

Interval 2 to 2 and 2 to 5 are adjacent, so combine both them with above concept

  22f(x)dx+25f(x)dx=25f(x)dx25f(x)dx21f(x)dx

The interval 2 to 1 is left end of interval 2 to 5

So

  21f(x)dx+15f(x)dx21f(x)dx21f(x)dx+15f(x)dx21f(x)dx=15f(x)dx

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