Thread: calculus help!!!

1. calculus help!!!

Hi,

1.) Let R be the region in the xy plane that is outside the circle x^2+y^2=1 but inside the circle x^2+y^2=2 . Evaluate the double integral

double integration over R {1/x^2+y^2}dA

2.) Evaluate the integrals
double integrals
integral 0 to infinite integral 0 to infinite {dydx/(1+x^2+y^2)^3/2)

sorry if it is difficult to understand in written pattern.

I will appreciate if any can help me and thanks again

2. Hi,
Originally Posted by Mr.Green
1.) Let R be the region in the xy plane that is outside the circle x^2+y^2=1 but inside the circle x^2+y^2=2 . Evaluate the double integral

double integration over R {1/x^2+y^2}dA

2.) Evaluate the integrals
double integrals
integral 0 to infinite integral 0 to infinite {dydx/(1+x^2+y^2)^3/2)
You should try switching to polar coordinates.

3. Originally Posted by Mr.Green

2.) integral 0 to infinite integral 0 to infinite {dydx/(1+x^2+y^2)^3/2)
Following up on flyingsquirrel's suggestion, we have that $\displaystyle x,y$ are taken in the first quadrant, hence $\displaystyle 0\le r<\infty,\,0\le\varphi\le\frac\pi2$ and the double integral becomes $\displaystyle \int_{0}^{\pi /2}{\int_{0}^{\infty }{\frac{r}{\left( 1+r^{2} \right)^{3/2}}\,dr}\,d\varphi }=\frac{\pi }{2}.$