Change of variables Definition and 208 Threads

I'm trying to evaluate the double integral \int \int \sqrt{x^2 + y^2} \, dA over the region R = [0,1] x [0,1] using change of variables. Well, after fooling around, I've got an answer. I set u = x^2, v =y^2, and then calculated the jacobian of T which was 1. The image transformation...

I'm trying to evaluate the double integral \int \int \sqrt{x^2 + y^2} \, dA over the region R = [0,1] x [0,1] using change of variables Now I know polar coordinates would be the most efficient way, and thus I could say r= \sqrt{x^2 + y^2} . Is this legal to use polar coordinates...

Can anyone give me any hints as to find a suitable change of variables for this integral. infinity / |dt/(a^2+t^2)^3/2 = | / -infinity =2/a^2 * integral below...

Let R be the region bounded by the graphs of x+y=1, x+y=2, 2x-3y=2, and 2x-3y+5. Use the change of variables: x=1/5(3u+v) y=1/5(2u-v) to evaluate the integral: \iint(2x-3y)\,dA I found the jachobian to be -1/5 and the limits of integration to be 1<=u<=2 2<=v<=5 so i set up...

Ok, i have a problem with this double integral. I am having a hard time finding the limits. The question is Evaluate \iint \frac{dx\,dy}{\sqrt{1+x+2y}}\ D = [0,1] x [0,1], by setting T(u,v) = (u, v/2) and evaluating the integral over D*, where T(D*)=D Can some one help me find the...

Does anyone know of any sources that explain change of variables for double integrals. Actually, I get the change of variables thing, but a few of our problems don't give us the transforms. I don't understand how to create these myself. Here is an example: Math Problem So far, I found...

Wacky change of variables for Multi integration! Arghh I am having diffiiculty with these problems. I am having difficulty mastering the LaTeX form--- (things like how to make a double integral etc) so if you look at this site...

im working on these, and I am supposed to find the image of a set under a given transformation. can someone please explain to me a good way of doing this?