Question

Find the volume of the solid using a triple integral.

The solid enclosed between the surfaces x = y^{2} +
z^{2} and x = 1 - y^{2}.

Answer #1

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Use a triple integral to find the volume of the given solid.
The tetrahedron enclosed by the coordinate planes and the
plane
11x + y + z = 2

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 cylindrical coordinates.
Find the volume of the solid that is enclosed by the cone
z =
x2 + y2
and the sphere
x2 + y2 + z2 = 128.

Write a triple integral including limits of integration that
gives the volume of the cap of the solid sphere x2+y2+z2≤34 cut off
by the plane z=5 and restricted to the first octant. (In your
integral, use theta, rho, and phi for θ, ρ and ϕ, as needed.)

Use a triple integral to find the volume of the solid under the
surfacez = x^2 yand above the triangle in the xy-plane with
vertices (1.2) , (2,1) and (4, 0).
a) Sketch the 2D region of integration in the xy plane
b) find the limit of integration for x, y ,z
c) solve the integral

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

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

1. Evaluate ???(triple integral) E
x + y dV
where E is the solid in the first octant that lies under the
paraboloid z−1+x2+y2 =0.
2.Evaluate ???(triple integral) square root ?x^2+y^2+z^2 dV
where E lies above the cone z = square root x^2+y^2 and between
the spheres x^2+y^2+z^2=1 and x^2+y^2+z^2=9

Find the volume of the solid by subtracting two volumes, the
solid enclosed by the parabolic cylinders
y = 1 − x2,
y = x2 − 1
and the planes
x + y + z = 2,
5x + 5y − z + 20 = 0.

1) Find the volume of the solid obtained by rotating the region
enclosed by the graphs about the given axis. ?=2?^(1/2), y=x about
y=6 (Use symbolic notation and fractions where needed.)
2) Find the volume of a solid obtained by rotating the region
enclosed by the graphs of ?=?^(−?), y=1−e^(−x), and x=0 about
y=4.5.
(Use symbolic notation and fractions where needed.)

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