# Double integral in polar form

1. Mar 8, 2006

### BananaMan

i have the integral $$\int_{0}^{\infty} \int_{0}^{\infty} (-x^2-y^2) \ dx dy$$
(double integral with both limits the same....assuming my first bash at the tex comes out

it says to transfer it into polar form and evaluate it

i have no idea how to convert a limit of infinity to polar form, help please

Last edited: Mar 8, 2006
2. Mar 8, 2006

### HallsofIvy

Staff Emeritus
Really? Your instructor has given you this problem without the slightest indication of what polar coordinates are? What an evil person! And you text book doesn't have anything about the "differential of area" in polar coordinates?? Are you sure you are reading it correctly?

3. Mar 9, 2006

### BananaMan

no, we have gone over polar co-ordinates, but never with an integration limit of infinity so i have no idea how to convert the limit to evaluate it

4. Mar 9, 2006

### TD

Make a skech of the integration area for x and y.
How can you cover the same area in polar coördinates?

5. Mar 9, 2006

### BananaMan

how do you sketch the area of x or y to infinity though?

6. Mar 9, 2006

### HallsofIvy

Staff Emeritus
Are you serious? x going from 0 to $\infty[/tex] and y going from 0 to [itex]\infty$ means that x and y may take on all non-negative values- the first quadrant. Now, what do r and $\theta$ range over in the first quadrant?