Question: Problem 4. This problem involves applying the divergence theorem to compute volumes.aSbe a closed smooth surface, and let E denote the region enclosed byS. Provethe
Problem 4. This problem involves applying the divergence theorem to compute volumes.aSbe a closed smooth surface, and let E denote the region enclosed byS. Provethe following relation:vol(E)=13SF*hat(n)dSwhere F=(:x,y,z:),vol(E) represents the volume ofE, and hat(n)is the unit outwardnormal vector to the surface S.bx2a2+y2b2+z2c2=1The natural parametrization of the ellipsoid is given by:r(,):={x=asin()cos()y=bsin()sin()z=ccos()where in[0,2] and in[0,].
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