http://calc3.askbot.com/questions/Open source question and answer forum written in Python and DjangoenCopyright Askbot, 2010-2011.Thu, 31 Jul 2014 11:16:48 -0500http://calc3.askbot.com/question/210/volume-integrals/I was wondering if when we are setting up volume integrals, if we always integrate as 1? then $\delta \rho \delta \phi \delta \theta$ ? or do we use the function, and then if it ends up being 1, we go with that? For example number 5 on the review sheet for the final exam. It says "Let S denote the unit sphere. Evaluate $$\iiint_S (x^2 + y^2 + z^2) dV$$ " So I was wondering if we set it up as... $$ \int _0 ^{2\pi} \int _0 ^\pi \int _0^1 \rho^2* \rho^2 \sin \phi \delta \rho \delta \phi \delta \theta $$ or $$ \int _0 ^ {2\pi} \int _0 ^\pi \int _0^1 1 * \rho^2 \sin \phi \delta \rho \delta \phi \delta \theta $$Thu, 31 Jul 2014 11:01:05 -0500http://calc3.askbot.com/question/210/volume-integrals/http://calc3.askbot.com/question/210/volume-integrals/?answer=212#post-id-212So the only time that you want to evaluate an integral representing the volume of $D$ is when it is specifically asked. For example question #$4e$ off of the in-class worksheet from July 24th. Otherwise, always use the function given and convert it to whatever coordinate system you are going to use. So for this problem it would be: $$\int_0^{2\pi}\int_0^{\pi}\int_0^1 (\rho^2)\rho^2 \sin(\phi) d\rho d\phi d\Theta$$Thu, 31 Jul 2014 11:16:48 -0500http://calc3.askbot.com/question/210/volume-integrals/?answer=212#post-id-212