Change of variable question

35 Views Asked by At

Let $D$ be the region in the first quadrant ($x>0$, $y>0$) of the $xy$-plane bounded by the curves

  • $y=\sqrt x$,
  • $y=2\sqrt x$,
  • $x^2+y^2=1$,
  • $x^2+y^2=4$.

Using a change of variables, evaluate the double integral
$$\int\int_D\frac{2x^2+y^2}{xy} dA.$$

I'm using change of variables u=$$\frac{y^2}{x}$$

and v = $$x^2 + y^2 $$

Using this, I found the value for what is basically $$\frac{1}{jacbobian}$$

but even with this, I can't seem to solve the integral.

Help is greatly appreciated.