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Stewart
For the unit ball \(S = \big\{(x,y,z) \mid x^2+y^2+z^2 \leq 1 \big\}\) evaluate\(\displaystyle \iiint_S \mathrm{e}^{(x^2+y^2+z^2)^{3/2}} \,\mathrm{d}V \) -
Stewart
Calculate the volume of the solid \(S\) that lies above the cone \(z = \sqrt{x^2+y^2}\) but below the sphere \(x^2+y^2+z^2=z.\) -
Dawkins
Evaluate \(\iiint_S 16z\,\mathrm{d}V\) where \(S\) is the upper half of the sphere of radius one centered at the origin. -
Dawkins
Evaluate the integral\(\displaystyle \int\limits_{0}^{3} \int\limits_{0}^{\sqrt{9-y^2}} \int\limits_{\sqrt{x^2+y^2}}^{\sqrt{18-x^2-y^2}} \Big(x^2+y^2+z^2\Big) \,\mathrm{d}z\,\mathrm{d}x\,\mathrm{d}y.\)