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Spherical Coordinates

  1. Aug 8, 2011 #1
    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. jcsd
  3. Aug 8, 2011 #2


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    Hi Mohammad! :smile:

    We usually write the volume element as sinθdrdθdφ because we use only 0 ≤ θ ≤ π …

    but the element is really |sinθdrdθdφ| …

    if you use that, your integral from 0 ≤ θ ≤ 2π will work :wink:
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