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 given solid. The
solid enclosed by the paraboloid x = 7y2 + 7z2 and the plane x =
12

Use a triple integral to find the volume of the solid enclosed
by the paraboloids y=x2+z2 and
y=50−x2−z2.

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

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

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.

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 by subtracting two volumes, the
solid enclosed by the parabolic cylinders
y = 1 − x2,
y = x2 − 1
and the planes
x + y + z = 2,
6x + 2y − z + 14 = 0.

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