Hello,
I solved these two problems, but I was wondering if somebody could tell me some trick to know whether to integrate with respect to x first or with respect to y first. I solved both by trial-and error; I tried both ways to see which one gave me the right answer.
11. f(x,y) = x/y over the region in the first quadrant bounded by the lines y = x, y = 2x, x =2.
15. f(u,v) = v - (sqrt)u over the triangular region cut from the first quadrant of the uv-plane by the line u + v = 1.
Again, I have no problem solving double integrals or deciding how to determine the limits of integration; I just want to know if I can tell ahead of time in which order I should be integrating. Does the one with variables as limits of integration always go on the inside?
Thanks!
I solved these two problems, but I was wondering if somebody could tell me some trick to know whether to integrate with respect to x first or with respect to y first. I solved both by trial-and error; I tried both ways to see which one gave me the right answer.
11. f(x,y) = x/y over the region in the first quadrant bounded by the lines y = x, y = 2x, x =2.
15. f(u,v) = v - (sqrt)u over the triangular region cut from the first quadrant of the uv-plane by the line u + v = 1.
Again, I have no problem solving double integrals or deciding how to determine the limits of integration; I just want to know if I can tell ahead of time in which order I should be integrating. Does the one with variables as limits of integration always go on the inside?
Thanks!
