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