Integration

Convert the equation into spherical coordinates.

\rho=18 \sec (\varphi)

\rho=18 \sin (\varphi)

x^{2}+y^{2}+(z-9)^{2}=81

\rho=\sqrt{18}

\rho=18 \cos (\varphi)

Integration

\left(\sqrt{26}, \frac{\pi}{6}, \frac{\pi}{3}\right)

Convert the spherical point (p, o, 0) into rectangular coordinates.

Integration

Convert the spherical point (p, q,0) into rectangular coordinates.

Integration

Set up and evaluate the indicated triple integral in the appropriate coordinate system. Enter an exactanswer. Do not use a decimal approximation.

\iiint_{Q} z d V, \text { where } Q \text { is the region between } z=\sqrt{x^{2}+y^{2}} \text { and } z=\sqrt{16-x^{2}-y^{2}}

\iiint_{Q} z d V=

Integration

After set up, evaluate the indicated triple integral in the appropriate coordinate system. Enter an exactanswer. Do not use a decimal approximation.

\iiint_{Q} z e^{f(x, y)} d V, f(x, y)=\sqrt{x^{2}+y^{2}}, \text { where } Q \text { is the region inside } x^{2}+y^{2}=100, \text { outside } x^{2}+y^{2}=64

and between z=0 and z=5.

\iiint_{Q} z e^{f(x, y)} d V=

Integration

\text { Set up the triple integral } \iiint_{Q} f(x, y, z) d V \text { in cylindrical coordinates. }

Q \text { is the region bounded by } y=36-x^{2}-z^{2} \text { and } y=3

\int_{0}^{6} \int_{3}^{36-r^{2}} \int_{0}^{2 \pi} f(r \cos (\theta), y, r \sin (\theta)) \cdot r d y d r d \theta

\int_{0}^{36} \int_{3}^{36-r^{2}} \int_{0}^{2 \pi} f(r \cos (\theta), y, r \sin (\theta)) \cdot r d y d r d \theta

\int_{0}^{6} \int_{0}^{2 \pi} \int_{3}^{36-r^{2}} f(r \cos (\theta), y, r \sin (\theta)) \cdot r d y d r d \theta

\int_{0}^{2 \pi} \int_{0}^{6} \int_{3}^{36-r^{2}} f(r \cos (\theta), y, r \sin (\theta)) \cdot r d y d r d \theta

Integration

\text { Set up the triple integral } \iiint_{Q} f(x, y, z) d V \text { in cylindrical coordinates. }

Q \text { is the region above } z=\sqrt{x^{2}+y^{2}} \text { and below } z=\sqrt{1352-x^{2}-y^{2}} .

\int_{0}^{2 \pi} \int_{0}^{26} \int_{r}^{\sqrt{1352-r^{2}}} f(r \cos (\theta), r \sin (\theta), z) d z d r d \theta

\int_{0}^{2 \pi} \int_{0}^{26} \int_{r}^{\sqrt{1352-r^{2}}} f(r \cos (\theta), r \sin (\theta), z) \cdot r d z d r d \theta

\int_{0}^{2 \pi} \int_{0}^{676} \int_{r}^{\sqrt{1352-r^{2}}} f(r \cos (\theta), r \sin (\theta), z) d z d r d \theta

\int_{0}^{2 \pi} \int_{0}^{676} \int_{\nu}^{\sqrt{1352-r^{2}}} f(r \cos (\theta), r \sin (\theta), z) \cdot r d z d r d \theta

Integration

Write the given equation in Cylindrical coordinates.

(x-95)^{2}+y^{2}=9,025

r=95 \sin (\theta)

r=95 \cos (\theta)

r=190 \sin (\theta)

r=190 \cos (\theta)

Integration

Write the given equation in cylindrical coordinates.

x^{2}+y^{2}=196

Integration

Find the mass of the solid with density p(x, y, z) and the given shape.

\rho(x, y, z)=41, \text { solid bounded by } z=x^{2}+y^{2} \text { and } z=9

Mass