# Thread: Find Area of the Region

1. ## Find Area of the Region

Find the area of the region bounded by the graphs of the equations.

y = x^3 + x, x = 2, y = 0.

I know how to set up the integral to solve this problem. Previous questions gave two values for x that became the upper and lower limits of integration. In this question, only one x value is given. What are the limits of integration here? I can then complete the problem.

2. ## Re: Find Area of the Region

Originally Posted by nycmath
Find the area of the region bounded by the graphs of the equations.

y = x^3 + x, x = 2, y = 0.

I know how to set up the integral to solve this problem. Previous questions gave two values for x that became the upper and lower limits of integration. In this question, only one x value is given. What are the limits of integration here? I can then complete the problem.
$\int_0^2 {({x^3} + x)dx}$

3. ## Re: Find Area of the Region

That was my second choice for x.

4. ## Re: Find Area of the Region

Originally Posted by nycmath
That was my second choice for x.
Well, that is the only bounded area.

5. ## Re: Find Area of the Region

Hello, nycmath!

Did you make a sketch?

Find the area of the region bounded by the graphs of the equations.
. . y = x^3 + x, .x = 2, .y = 0.

What are the limits of integration here?

The graph looks like this:

Code:
              |
|      *
|      '
|     *'
|   .*:'
| .*:::'
- - - - * - - -+- -
*  |      2
*    |
*     |
|
*      |
|
Can you see the limits now?

6. ## Re: Find Area of the Region

Thanks everyone.

7. ## Re: Find Area of the Region

Originally Posted by Soroban
Hello, nycmath!

Did you make a sketch?

The graph looks like this:

Code:
              |
|      *
|      '
|     *'
|   .*:'
| .*:::'
- - - - * - - -+- -
*  |      2
*    |
*     |
|
*      |
|
Can you see the limits now?
The limits are [0,2]. Soroban, check your inbox.