- Consider the iterated triple integral $$V=\iiint_D dV=\int_{-3}^{3}\int_{0}^{\sqrt{9-y^2}}\int_{0}^{9-x^2-y^2}dzdxdy.$$ This integral gives the volume of the solid $D$ in space described by the bounds of the integral.
- Draw the region described by the bounds of this integral.
- Set up the integral using the order of integration $dydxdz$.
- Set up the integral using the order of integration $dxdydz$.
- Set up the integral using cylindrical coordinates (any order is fine).
- Consider the iterated triple integral $$V=\iiint_D dV=\int_{-1}^{1}\int_{0}^{1-x^2}\int_{0}^{y}dzdydx.$$
- Draw the region described by the bounds of this integral.
- Set up the integral using the order of integration $dydzdx$.
- Set up the integral using the order of integration $dxdydz$.
- Use a triple integral with spherical coordinates to find the volume of a hemiball of radius $a$ (so the region under the sphere $x^2+y^2+z^2=a^2$ and above the $xy$-plane). Note that $dV=\rho^2\sin\phi d\rho d\phi d\theta$.
|
Sun |
Mon |
Tue |
Wed |
Thu |
Fri |
Sat |