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Stewart
Evaluate \(\iiint_S x^2 \,\mathrm{d}V\) for the solid \(S\) that lies under the paraboloid \(z=4-x^2-y^2\) and above the \(xy\)-plane. -
Stewart
A solid \(S\) lies within the cylinder \(x^2+y^2=1\) on the positive \(y\) side of the \(xz\)-plane, below the plane \(z=4,\) and above the paraboloid \(z=1-x^2-y^2.\) The density at any point in the solid is three times its distance to the \(z\)-axis. What is the mass of \(S?\) -
Stewart
Evaluate this iterated integral:\(\displaystyle \int\limits_{-2}^{2} \int\limits_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}} \int\limits_{\sqrt{x^2+y^2}}^{2} \Big(x^2 + y^2\Big) \,\mathrm{d}z \,\mathrm{d}y \,\mathrm{d}x \) -
Review
What are the spherical coordinates \((\rho,\theta,\phi)\) of a point in \(\mathbf{R}^3\) with rectangular coordinates \((x,y,z)=(8,-4,3)?\) -
Review
What are the rectangular coordinates \((x,y,z)\) of a point in \(\mathbf{R}^3\) with spherical coordinates \((\rho,\theta,\phi)=(5,5\pi/3,5\pi/6)?\)