integration

Questions & Answers

Question 42010

Verified

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)

Question 42009

Verified

Integration

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

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

Question 42008

Verified

Integration

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

Question 42007

Verified

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=

Question 42006

Verified

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=

Question 42005

Verified

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

Question 42004

Verified

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

Question 42003

Verified

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)

Question 42002

Verified

Integration

Write the given equation in cylindrical coordinates.

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

Question 42001

Verified

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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