Question

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

Answer #1

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

Find the volume of the solid using a triple
integral.
The solid enclosed between the surfaces x = y2 +
z2 and x = 1 - y2.

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

Use Divergence theorem to evaluate surface integral S F ·n dA
where S is the surface of the solid enclosed by the tetrahedron
formed by the coordinate planes x = 0, y = 0 and z = 0 and the
plane 2x + 2y + z = 6 and F = 2x i − x^2 j + (z − 2x + 2y) k.

6. Let R be the tetrahedron in the first octant bounded by the
coordinate planes and the plane passing through (1, 0, 0), (0, 1,
0), and (0, 0, 2) with equation 2x + 2y + z = 2, as shown below.
Using rectangular coordinates, set up the triple integral to find
the volume of R in each of the two following variable orders, but
DO NOT EVALUATE.
(a) triple integral 1 dxdydz
(b) triple integral of 1 dzdydx

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.

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

Please answer ASAP
Find the volume of the solid by subtracting two volumes, the
solid enclosed by the parabolic cylinders y = 1
- x 2, y = x
2 - 1 and the planes x + y +
z = 2, 4x + 3y - z + 18 =
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.

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