What would be my bounds of integration if I'm trying to integrate a function f(x,y) over a region bounded by y = x and y = -x^{2} ?
Giest
It's not quite simple as that. The multivariate function that I'm integrating requires two iterated integrals, and the bounds for the inner integrand, I'm pretty sure, need to expressed as a function of one of the two variables.
If you have a double integral like this
$\displaystyle \int^a_b (\int^c_d f(x,y) dy)dx$
The limits c and d on the y integral are c=x and d=-x^{2}
The limits a and b on the x integral are a=0 and b=-1 as minoanman shows in his graph
You may wonder why I said c=x and d=-x^{2} not d=x and c=-x^{2}. x is always higher than -x^{2} and you want to integrate in the positive direction of y so the integral limits are FROM the lower value TO the higher value.
I didn't mean to waste anyone's time. I just thought I'd keep things simple by giving the part of the problem that was putting me off--that and the fact it takes me a long time to do anything in LaTex. But I'll keep that in mind next time.