# Thread: Finding the Area of an Enclosed Region

1. ## Finding the Area of an Enclosed Region

How would I solve this problem...

What is the area of the region enclosed by the graphs of $\displaystyle f(x)=x-2x^2$ and $\displaystyle g(x)=-5x$?

2. Originally Posted by summermagic
how would i solve this problem...

What is the area of the region enclosed by the graphs of $\displaystyle f(x)=x-2x^2$ and $\displaystyle g(x)=-5x$?

The area between curves is upper - lower

$\displaystyle \int_{0}^{3}(x-2x^2)-(-5x)dx=-2 \int_{0}^{3} (x^2-3x)dx...$

3. Hello, summermagic!

I don't suppose you made a sketch . . .

Find the area of the region enclosed by the graphs of $\displaystyle f(x)=x-2x^2$ and $\displaystyle g(x)=-5x$
Code:
          |
*   |
* |  ..*..
- - - *::::::::*- - - - - - -
* | *::::::::*
*  |   *:::::::*
|     *::::::.
*   |       *::::*
|         *:::.
|           *::
*    |             *
|

The graphs intersect at (0,0) and (-3,-15).

You must evaluate: .$\displaystyle \int^3_0\bigg[(x-2x^2) - (-5x)\bigg]\,dx$