# Thread: Find the area between two curves

1. ## Find the area between two curves

Any help with the following problem would be greatly appreciated!

Find the area enclosed by the given curves.

8x+y^2= 15
x=y

I've been told to find the points of intersection and integrate with respect to y. I'm not exactly sure how to proceed.

2. Originally Posted by vlodge
Any help with the following problem would be greatly appreciated!

Find the area enclosed by the given curves.

8x+y^2= 15
x=y

I've been told to find the points of intersection and integrate with respect to y. I'm not exactly sure how to proceed.
Graph it out and it will be easy to see your bounds of integration.

3. Originally Posted by vlodge
Any help with the following problem would be greatly appreciated!

Find the area enclosed by the given curves.

8x+y^2= 15
x=y

I've been told to find the points of intersection and integrate with respect to y. I'm not exactly sure how to proceed.
sure you have the equations correct? ... the points of intersection are not pretty.

$\displaystyle x = \frac{15-y^2}{8}$

$\displaystyle x = y$

$\displaystyle y = \frac{15-y^2}{8}$

$\displaystyle 8y = 15 - y^2$

$\displaystyle y^2 + 8y - 15 = 0$

$\displaystyle y = -4 \pm \sqrt{31}$

$\displaystyle A = \int_{-4 - \sqrt{31}}^{-4 + \sqrt{31}} \frac{15-y^2}{8} - y \, dy$