Question

triple integrals Find the average value of the function ?(?, ?, ?) = 5? + 3? over the solid tetrahedron bounded by the planes ? = 0, ? = 0, ? = 0, and ? + ? + 2? = 2.

Answer #1

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.

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.

Use triple integrals to calculate the average value of F(x,y,z)
over the given region:
F(x,y,z) = xyz
on the cube in the first octant delimited by the coordinate
planes and the planes
x = 1, y = 1, z = 1

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

Using triple integrals, find the volume bounded by the cylinder
y=9-x2 and the paraboloid
y=2x2+3z2.

3. Use double integrals to find the center of mass, (xcm, ycm),
of a lamina with density function ρ = x bounded by y = x^2 , x = 0
and y = 1.

In the Midpoint Rule for triple integrals we use a triple
Riemann sum to approximate a triple integral over a box B, where
f(x, y, z) is evaluated at the center (xi, yj, zk) of the box Bijk.
Use the Midpoint Rule to estimate the value of the integral. Divide
B into eight sub-boxes of equal size. (Round your answer to three
decimal places.) cos(xyz) dV, where B = {(x, y, z) | 0 ≤ x ≤ 5, 0 ≤...

In the Midpoint Rule for triple integrals we
use a triple Riemann sum to approximate a triple integral over a
box B, where
f(x, y, z)
is evaluated at the center
(xi, yj, zk)
of the box
Bijk.
Use the Midpoint Rule to estimate the value of the integral.
Divide B into eight sub-boxes of equal size. (Round your
answer to three decimal places.)
cos(xyz) dV, where B = {(x, y, z) | 0 ≤ x ≤ 2, 0 ≤...

Find the integral that represents the volume of the solid
bounded by the planes y = 0, z = 0, y = x and 6x + 2y + 3z = 6
using double integrals.

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