Find the area of the region enclosed by the given curves:

4x+y^2=9, x=2y

3 answers

First, find where they intersect.

4x+y^2=9, x=2y
4(2y) + y^2 = 9
y^2 + 8y - 9 = 0
(y+9)(y-1) = 0

So, it might be easier to integrate in the y-direction:

∫[-9,1] (y^2-9)/4 - 2y dy
∫[-9,1] y^2/4 - 2y - 9/4 dy
y^3/12 - y^2 - 9/4 y [-9,1]
(-729/12 - 81 + 81/4) - (1/12 - 1 - 9/4)
355/3
Unfortunately, that answer is not right...

This is the last problem on my homework and I've been stuck on it for about an hour. Its very frustrating
How about 125/3 ?

If you had read my posting carefully (as I did not) you'd have noticed that it should have been

(9-y^2)/4