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Math Help - Area of ellipsoid, working out the limits?

  1. #1
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    Area of ellipsoid, working out the limits?

    I know the general method for this question, but I'm struggling with finding limits on \theta and \phi

    Calculate the area of the portion E_+ of the ellipsoid \frac{x^2}{4}+\frac{y^2}{4}+z^2=1 that lies above the xy plane by making use of the parameterisation r(\theta,\phi) = (2\cos{\phi}\sin{\theta},2\sin{\phi}\sin{\theta},\  cos{\theta})

    What I've got is that because it lies above the xy plane, we have z\geq0 so cos{\theta}\geq0 \implies 0\leq\theta\leq\frac{\pi}{2}
    I don't think there is any restriction on \phi so we have 0\leq\phi\leq2\pi

    ?
    Last edited by cana; May 20th 2011 at 03:28 AM.
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  2. #2
    MHF Contributor
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    You may wish to consider symmetries and just work in the 1st octant.
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