# Thread: area under a curve

1. ## area under a curve

Find the area bounded by the curves, y1= -3x+4 and y2= -2x+3 on the interval [-4,5].

2. Hello, singh!

Find the area bounded by the curves: . $\begin{array}{c}y\:=\:-3x+4 \\ y\:=\: -2x+3\end{array}$ . on the interval [-4,5]

I hope you made a sketch!
Code:
      *         |
*       |
|:*.    |
*   |:::*.  |
*:::::*.|
|   *:::*.
|       * *             5
- - + - - - + - *.- - - - - + - -
-4       |     *:*.      |
|       *:::*.  |
|         *:::::*
|           * ::|   *
|             *:|       *
|               *
|                 *

3. so would the area be zero since the negative region and the positive region cancel out?

4. Areas cannot be negative, so they never 'cancel' themselves out.

5. Originally Posted by DivideBy0
Areas cannot be negative, so they never 'cancel' themselves out.
I agree with you in terms of this problem, but note that if we take the integral
$\int_0^{\pi/2}cos(x)~dx = 0$
because the "negative region and the positive region cancel out." It all depends on what the kind of problem is that you are doing. (I suppose the difference is that the above problem is an integral, not specifying that we are trying to find an area.)

-Dan