Quick question on double/triple integrals for area and volume

[Lifprasir]

I do not know how to formulate formulas on this forum so I just wrote it neatly on a piece of paper and linked it.

http://puu.sh/8fwXr.jpg

Thankss.

 

[Mark44]

Would you edit your post to attach a new image that is smaller? The maximum width should be about 900 pixels. Yours is about 1200 pixels, so doesn't fit in the window.

To answer your question. If f(x, y) = 0, then the integral will be zero.

$\int \int 0 dA = \int \int 0 r dr d\theta = 0$

If the integrand is identically zero for any kind of integral, then the value of the integral is zero.