# SOLVED: (d): Use triple integral in cylindrical coordinates to evaluate dzdydx. (e): Use triple integral in spherical coordinates to evaluate âˆ¬âˆ¬âˆ¬ R dV where R is the ball given by R=(x,y,z)

Calculus 3 Lecture 14.7: TRIPLE Integrals Over Regions with CYLINDRICAL or SPHERICAL Coord.
Calculus 3 Lecture 14.7: TRIPLE Integrals Over Regions with CYLINDRICAL or SPHERICAL Coord.

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(d): Use triple integral in cylindrical coordinates to evaluate dzdydx.
(e): Use triple integral in spherical coordinates to evaluate âˆ¬âˆ¬âˆ¬ R dV where R is the ball given by R={(x,y,z) | x^2 + y^2 + z^2 < 4}.
(f): Use triple integral in spherical coordinates to find the volume of the solid that is enclosed by the cone z = r + y and the sphere x^2 + y^2 + z^2 = 2.

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12:26

(a) find the spherical coordinate limits for the integral that calculates the volume of the given solid and then (b) evaluate the integral.The solid bounded below by the sphere $\rho=2 \cos \phi$ and above by the cone $z=\sqrt{x^{2}+y^{2}}$

06:13

Set up and evaluate a triple integral in spherical coordinates to find the volume of the solid that lies above the cone z = âˆš(x^2 + y^2) and below the sphere x^2 + y^2 + (z-2)^2 = 2.

02:31

Find the volume using a triple integral in sphericalcoordinates of the solid bounded above the spherex^2+y^2+z^2=4 and below the cone z^2=x^2+y^2

11:04

Use spherical coordinates to calculate the triple integralfor volume of the solid E above the xyplane, inside the spherewith equation x^2 + y^2 + z^2 = 4 and below the paraboloid withequation 3z = x^2 + y^2 .

01:47

Compute the value of âˆ G dV where G is the solid bounded above by the sphere x^2 + y^2 + z^2 = 4 and below by the cone z = âˆš(x^2 + y^2) (Hint: Use spherical coordinates)

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