Question

Using triple integrals, find the volume bounded by the cylinder
y=9-x^{2} and the paraboloid
y=2x^{2}+3z^{2}.

Answer #1

Use triple integral and find the volume of the solid E bounded
by the paraboloid z = 2x2 + 2y2 and the plane
z = 8.

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

. Find the volume of the solid bounded by the cylinder x 2 + y 2
= 1, the paraboloid z = x 2 + y 2 , and the plane x + z = 5

Find the volume of the solid that lies under the paraboloid
z=2x2+2y2 above the xy-plane, and inside the
cylinder x2+y2=8y

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.

Use triple integration to find the volume of the solid cylinder
x^2 + y^2 = 9 that lies above z = 0 and below x + z = 4.

Find the volume of the solid bounded by the cylinder x^2+y^2=9
and the planes z=-10 and 1=2x+3y-z

Find the volume of the region below the paraboloid z = 2 +
x2 + (y – 2)2 and above the hyperbolic
paraboloid z = xy over the rectangle R = [–1, 1] ´ [1, 4].

draw the solid bounded above z=9/2-x2-y2
and bounded below x+y+z=1. Find the volume of this
solid.

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.

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