1. ## Double integral problem

Hi, I am having trouble with the following:

Find the double integral of x+y, bounded by y=1 and y=x^2.

I know the y integral will be between 0 and 1, but what will the x integral bounds be? because from what I can see by drawing the graph is that both the upper and lower bounds are y=x^2, but that doesn't make any sense.

2. ## Re: Double integral problem

I always have to draw a graph for these - or at least imagine one. You have a parabola and a horizontal line; the intersections are (-1,1) and (1,1). You get to choose whether to integrate y first or x first - I would have gone with y first, but it looks like you're doing x first. The right and left boundaries are the parabola, so solving for x gives $\displaystyle x=-\sqrt{y}$ and $\displaystyle x=\sqrt{y}$. Then y goes from 0 to 1, as you said.

If you integrate with respect to y first, then the top and bottom boundaries are the line and the parabola, so y goes from $\displaystyle x^2$ to 1. And then x goes from -1 to 1.

- Hollywood