Green's Theorem Question! If you have a triangle that intersects these points: (0,0), (4,5), (0,5) and goes back to (0,0) again, when you are trying to find the bounds for a double integral, what do you do? I know that one of the bounds is from 0 to 5, and the other starts with zero, but I don't know how to get the upper bound.

Question

Green's Theorem Question! If you have a triangle that intersects these points: (0,0), (4,5), (0,5) and goes back to (0,0) again, when you are trying to find the bounds for a double integral, what do you do?  I know that one of the bounds is from 0 to 5, and the other starts with zero, but I don't know how to get the upper bound.

mr.math · Answer

I think the limits are $0<x<\frac{4}{5}y$ and $0<y<5$.

anonymous · Answer

Hmm...I have been working on this and I think you are right, except for I think it is supposed to be 0<x<5/4y. Rise/run, yes?

mr.math · Answer

I don't think so. You can write it as $0<x<4$ and $0<y<\frac{5}{4}x$, it's the same thing. The line that bounds the region from the right is y=(5/4)x.

anonymous · Answer

Oh, okay, so I had y= (5/4)x, but when you have that, you have to integrate by dx first?

mr.math · Answer

It should be something like this, if you go with the second option:
$$\int\limits_0^4 \int\limits_0^{\frac{5}{4}x} f(x,y)dydx$$

mr.math · Answer

Does this make sense to you?

anonymous · Answer

Yes, thanks so much for helping! I am finally doing the integral right XD

mr.math · Answer

Best of luck :)