Suppose $f(x,y,z)=1/\sqrt{x^2+y^2+z^2}$ and $W$ is the bottom half of a sphere of radius $5$.

(a) As an iterated integral, we can write

$$\iiint_WfdV=\int_{A}^{B}\int_{C}^{D}\int_{E}^{F} d\rho d\varphi d\theta$$

What are the values of $(A,B,C,D,E,F)$?

  • 1
    $\begingroup$ What is your question? $\endgroup$ – Dennis Gulko Mar 24 '13 at 22:36
  • $\begingroup$ Please check that the edit is what you intended. $\endgroup$ – Stahl Mar 24 '13 at 22:37
  • $\begingroup$ The integral in the question is equal to $\int_0^5\rho d\rho\int_0^{\pi/2}\sin\theta d\theta\int_0^{2\pi}d\phi=25\pi$. I'm still not sure what $(A,B)$ etc. mean, though. $\endgroup$ – John Gowers Mar 24 '13 at 22:43
  • $\begingroup$ I asking to solve the iterated integral and find the valuse of A,B,C,D,E,F which are limits of integration $\endgroup$ – Michael Rametta Mar 25 '13 at 0:43
  • $\begingroup$ @MichaelRametta: See the edit. Is this what you mean? $\endgroup$ – Mhenni Benghorbal Mar 25 '13 at 0:46

$$ \iiint_WfdV=\int_{0}^{2\pi} \int_{\pi/2}^{\pi}\int_{0}^{5}\frac{1}{\rho}\rho^2 \sin(\phi)d \rho \,d\phi\,d\theta\, $$

where $\phi$ is the angle with the $z$-axis.

  • $\begingroup$ Awsome. I understand now. Thanks for your time. Im new to this so Im trying to learn and just posting random questions from the book. I am taking this course this summer so wanted to prep for it. $\endgroup$ – Michael Rametta Mar 26 '13 at 0:40
  • $\begingroup$ @MichaelRametta: You are welcome. Good luck with your course. $\endgroup$ – Mhenni Benghorbal Mar 26 '13 at 2:29

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