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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)

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Integration

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

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

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Integration

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

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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=

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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=

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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

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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

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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)

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Integration

Write the given equation in cylindrical coordinates.

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

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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

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