Question

does integral ( integral ( (x-y)/(x^2+y*2) ) ) converges or not? (it is double integral) I have this exercise I don't know how to do it I even don't know what does that means , so please help

Answer 1

The integral is over what set of R^2 ?

Answer 2

oh sorry forgot so x+y>1 , x>0 , y>0

Answer 3

the denominator ..x^2+y^2 is it power or multiplication

Answer 4

@onikadze

Answer 5

it is power

Answer 6

hmm... kk

Answer 7

@onikadze whts the ans given i am doing same sums soo.... can give the ans

Answer 8

shall I tell you answer?

Answer 9

okay the answer is that it is not converged

Answer 10

here is the way how it was solved 35 th exersise

Answer 11

@shkrina

Answer 12

@onikadze i am sorry i have just stared that it too deep ... they can help u @amistre64 @mathstudent55 @Luigi0210

Answer 13

okay thanks anyway

Answer 14

@cwrw238

Answer 15

@Jhannybean

Answer 16

\[\int\int_{\Omega}\frac{x-y}{x^2+y^2}~dx~dy\]
with \(\Omega:=\left\{(x,y)~|~x+y>1,~x>0,~y>0\right\}\).

Here's a sketch of the region \(\Omega\):

Converting to polar coordinates, your integral becomes
\[\int\int_{\Omega}\frac{r\cos\phi-r\sin\phi}{r^2}~dr~d\phi\]