Evaluate the integral $\int x\,dV$ inside domain $V$, where $V$ is bounded by the planes $x=0$, $y=x$, $z=0$, and the surface $x^2+y^2+z^2=1$.
Answer given: $\dfrac{1}{8} - \dfrac{\sqrt{2}}{16}$
Uh, so I did it in spherical coordinates, which equals
$\iiint p^2 \sin φ \;dp dφ dθ$
$∫dp$ runs from $0$ to $1$
$∫dφ$ runs from $0$ to $\frac{\pi}{2}$ (right??)
$∫dθ$ runs from $-\frac{\pi}{2}$ to $\frac{\pi}{4}$ (because of the line $y = x$ in the $xy$ plane)
I do not get the given answer though.