Question

Use the triple integrals and spherical coordinates to find the volume of the solid that is bounded by the graphs of the given equations. x^2+y^2=4, y=x, y=sqrt(3)x, z=0, in first octant.

Answer #1

) Use spherical coordinates to find the volume of the solid
situated below x^2 + y ^2 + z ^2 = 1 and above z = sqrt (x ^2 + y
^2) and lying in the first octant.

Find the volume of the solid using triple integrals. The solid
region Q cut from the sphere x^2+y^2+z^2=4 by the cylinder r=2sinϑ.
Find and sketch the solid and the region of integration R. Setup
the triple integral in Cartesian coordinates. Setup the triple
integral in Spherical coordinates. Setup the triple integral in
Cylindrical coordinates. Evaluate the iterated integral

Use a double integral in polar coordinates to find the volume of
the solid bounded by the graphs of the equations.
z = xy2, x2 + y2 =
25, x>0, y>0, z>0

Use cylindrical coordinates to find the volume of the solid
bounded by the graphs of z = 68 − x^2 − y^2 and z = 4.

use a double integral in polar coordinates to find the volume of
the solid in the first octant enclosed by the ellipsoid
9x^2+9y^2+4z^2=36 and the planes x=sqrt3 y, x=0, z=0

Find 6 different iterated triple integrals for the volume of the
tetrahedron cut from the first octant (when x > 0, y > 0, and
z > 0) by the plane 6x + 2y + 3z = 6. Dont evaluate the
integrals.

1- Set up the triple integral for the volume of the sphere Q=8
in rectangular coordinates.
2- Find the volume of the indicated region.
the solid cut from the first octant by the surface z= 64 - x^2
-y
3- Write an iterated triple integral in the order dz dy dx for
the volume of the region in the first octant enclosed by the
cylinder x^2+y^2=16 and the plane z=10

Find the volume of the solid generated by revolving the region
bounded by the graphs of the equations about the
x-axis.
y = 1 / sqrt of (7x+3)
x = 0
y = 0
x = 7

Set up a triple integral in cylindrical coordinates to compute
the volume of the solid bounded between the cone z 2 = x 2 + y 2
and the two planes z = 1 and z = 2.
Note: Please write clearly. That had been a big problem for me
lately. no cursive Thanks.

Set up (Do Not Evaluate) a triple integral that yields the
volume of the solid that is below
the sphere x^2+y^2+z^2=8
and above the cone z^2=1/3(x^2+y^2)
a) Rectangular coordinates
b) Cylindrical
coordinates
c) Spherical
coordinates

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