Question

Find the area of the region between the curves 4x+y^2=12 and x=y.

Answer 1

I know you have to take the integral of each and subtract the area between the curves. I solved the first for y, getting sqrt(12-4x). I know that they intersect at 2 and that the first one is on top. This would mean \[\int\limits_{0}^{2} \sqrt{12-4x}dx-\int\limits_{0}^{2}xdx\]. However, I have solved it many times getting different answers, although once it matched the answer that I got from a website, but when I plug it into my homework online, it says it is incorrect. Help!

Answer 2

start by sketching them out.

Answer 3

were you given bounds?

Answer 4

here is what it looks like.

Answer 5

I assumed it was that top triangle shape in the first quadrant, but maybe it is the one below.

Answer 6

assuming you are bounded by the x and y axis you only look at this region, but you already know that