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

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 $(A,B,C,D,E,F)$?

• What is your question? – Dennis Gulko Mar 24 '13 at 22:36
• Please check that the edit is what you intended. – Stahl Mar 24 '13 at 22:37
• 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. – John Gowers Mar 24 '13 at 22:43
• I asking to solve the iterated integral and find the valuse of A,B,C,D,E,F which are limits of integration – Michael Rametta Mar 25 '13 at 0:43
• @MichaelRametta: See the edit. Is this what you mean? – 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.