Word Count : 287

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The given ellipsoid is [ \frac{x^2}{4} + \frac{y^2}{9} + \frac{z^2}{16} = 1. ] We want the volume using double integration. Solve for (z) in terms of (x) and (y): [ z^2 = 16 \left(1 - \frac{x^2}{4} - \frac{y^2}{9}\right) \implies z = \pm 4 \sqrt{1 - \frac{x^2}{4} - \frac{y^2}{9}}. ] The volume is [ V = \iint_R 2 ___ ____ ___ ________ ______ ________ _____ ______ ___ __________ ____.
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