How Do I Set Up Limits for a Double Integral Over a Triangular Region?

[ju0020]

Homework Statement

I'm supposed to solve a definite double integral. It's supposed to be in the area of the triangle with vertexes at (0,0), (1,1),(0,2)

Homework Equations

integral of
e^(y^2) * dy*dx

The Attempt at a Solution

First, I need to know the limits of x and y...
So, that triangle is defined by the lines x=y, x=0 and y=-x+2
with that I can define the limits for my integral

(ps. I don't know how to use latex very well so this will look kind of weird, but what's on top is the upper limit and what is under that is the lower limit).

I've tried it in the order $$\int$$$$\stackrel{1}{0}$$ $$\int$$$$\stackrel{-x+2}{x}$$ e^(y^2)*dy*dx
and $$\int$$$$\stackrel{1}{0}$$ $$\int$$$$\stackrel{y}{0}$$ e^(y^2)*dx*dy + $$\int$$$$\stackrel{2}{1}$$ $$\int$$$$\stackrel{0}{2-y}$$ e^(y^2)*dx*dy
But it both cases at some point I can't solve it. For example, in the second option I end up with an integral of 2*e^(y^2) and in the first option I can't even begin to solve that integral


I have a test in a few hours so any help is much appreciated. Thanks

 

[LCKurtz]

The limits on your very last integral are reversed, should be 0 to 2-y. You have the right idea about trying a dxdy integral, and the first one of the dx dy integrals works. You are correct the second one can't be worked. The problem might be miscopied or mis-stated such that the third point should have been (0,1), in which case you would have gotten it. Don't worry about it for the exam, you are good to go on that topic.