# The integral of ∫ − 3 0 ( 1 + 9 − x 2 ) 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 35E
To determine

## To Find: The integral of ∫−30(1+9−x2)dx

Expert Solution

The integral of 30(1+9x2)dx=94π+3

### Explanation of Solution

Given information:

The integral is:

30(1+9x2)dx

Calculation:

30(1+9x2)dx

Interpret this integral as the area under the curve y=4x2 from -3to2

But since

y=1+9x2y1=9x2x2+(y1)2=9

Which show the graph of f(x) is the quarter circle above xaxis with radius 3 in figure

Here, one rectangle with area =3

30(1+9x2)dx

= Area of quarter circle + Area of rectangle

30(1+9x2)dx=94π+3

Hence,

The integral of 30(1+9x2)dx=94π+3

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