]This isn't a home work question in particular, but just want confirmation about a general idea.(adsbygoogle = window.adsbygoogle || []).push({});

So in Calc III, you have integrals of the form

[tex]\int_{-a}^a \int_{-\sqrt{a^2 - x^2}}^{\sqrt{a^2 - x^2}} x y dy dx[/tex]

which is the typical rectangular coordinates for a circle. Now, the integrand is the term x y, and you sum over the pieces in the circle, you'll have for each piece a negative and a positive part, which will sum to zero. And since this holds for all pieces, then the integral will be zero.

My question is basically, what kind of rule of thumb can you use to check if the integralactually is zeroversus some still mistake on your part? I would assume that if x and y are both odd powers of a polynomial then you'll always have these opposing pairs. Is that correct?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Question about double (and triple) integrals over a symmetric area

**Physics Forums | Science Articles, Homework Help, Discussion**