# Math Help - double integrals

1. ## double integrals

Could someone go through this step step by step?
I get stuck at part ii

Thanks

2. Originally Posted by bille
Could someone go through this step step by step?
I get stuck at part ii

Thanks
Assuming that you have done part (i), the essential next step is to draw a diagram of the domain D. That should enable you to describe D in terms of u and v, namely that D is enclosed by the lines $u=1$, $u=e$, $v=0$ and $v=\pi$. The change of variables formula then tells you that the integral is equal to

. . . . . $\displaystyle\int_1^e\int_0^\pi\frac{\sin v}{x^2}\,\frac{x^2}u\,dvdu$.

The " $x^2$"s conveniently cancel, and from then on the integral should be easy.

3. Sorry, what is the change of variable formula?

4. Originally Posted by bille
Sorry, what is the change of variable formula?
The formula says that if you make a change of variables from (x,y) to (u,v), so that f(x,y) becomes g(u,v), then the integral $\displaystyle\iint_Df(x,y)\,dxdy$ becomes $\displaystyle\iint_Dg(u,v)\left|\frac{\partial(x,y )}{\partial(u,v)}\right|dudv$.

See here for more on this topic. (But if you are being asked to do problems like this, then presumably it is expected that you already know this stuff.)