- #1

Eclair_de_XII

- 1,083

- 91

- Homework Statement
- \begin{eqnarray}

0\leq z\leq \sqrt{x^2+y^2}\\

0\leq y\leq x\\

0\leq x\leq 1

\end{eqnarray}

##f(x,y,z)=\frac{(x^2+y^2)^\frac{3}{2}}{x^2+y^2+z^2}##

- Relevant Equations
- \begin{eqnarray}

x=\rho\cos\theta\cos\phi\\

y=\rho\sin\theta\cos\phi\\

z=\rho\sin\phi

\end{eqnarray}

Answer given in book: ##\frac{\pi}{12}##

Answer derived: ##\frac{3}{16}{\pi}##

I'm going to type out my LaTeX solution later on. But in the meantime, can anyone check my work? I know it's sloppy, disorganized, and skips far more steps than I care to count, but I'd very much appreciate it. I'm not getting the answer as given in the book. I think I failed this time because I assumed that ##\phi## was the angle from the x-axis (or any other axis that can be constructed with a line on the xy-plane) to some arbitrary point on the zx-plane. When I retried it while treating ##\phi## as the angle from the z-axis to some arbitrary point on the zx-plane, I got ##\frac{3}{4}\pi(\frac{\pi}{8}-1)##. Can anyone point out anything I might have done wrong in the photograph I posted while I type out a LaTeX version of my second attempt? Thank you.