Is this sound reasoning?
asked 2014-07-16 21:23:15 -0600
For problem 15 part b. The question asks if $$\int_{0}^{1} \int_{0}^{1} \sin(xy)dxdy$$ is positive or negative.
It seems like since both $x$ and $y$ are contained between zero and one that $xy$ will always be between zero and one.
This means that $\sin(f(x,y))$ will only have a positive argument in this section of the plot and therefore will only yield positive z values which means the integral is positive.
That seems reasonable to me but I'm wrong more often than I'm right when I try to reason this way and also the question just feels like a trick. What do you guys think?
