Spherical Coordinates

1. Aug 8, 2011

MHD93

I wanted to derive the volume of a sphere using triple integration with spherical coordinates, but instead of taking the limits of θ as (0° ≤ θ ≤ 180°), I chose to take (0° ≤ θ ≤ 360°), and therefore, for φ as (0° ≤ φ < 180°),

Now of course the integral of sin(θ) from 0° to 360° is zero, and the derivation failed..

Shouldn't it be the same result, why.. ?
Thank you

2. Aug 8, 2011