Question

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. No need to solve the integral.

Answer #1

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.

find the double integral that represents the
volume of the solid entrapped by the planes y=0, z=0, y=x and
6x+2y+3z=6 (please explain how to get the limits of integration)
you don't need to solve the integral just leave it expressed

Find the volume of the solid which is bounded by the cylinder
x^2 + y^2 = 4 and the planes z = 0 and z = 3 − y. Partial credit
for the correct integral setup in cylindrical coordinates.

Use a double integral in polar coordinates to find the volume of
the solid bounded by the graphs of the equations.
z = xy2, x2 + y2 =
25, x>0, y>0, z>0

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

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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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Write the triple integral in all 6 ways.

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The volume of the solid under the cone z = sqrt(x^2 + y^2) and
over the ring 4 ≤ x^2 + y^2 ≤ 25
The volume of the solid under the plane 6x + 4y + z = 12 and
on the disk with boundary x2 + y2 = y.
The area of the smallest region, enclosed by the spiral rθ =
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Find the volume of the solid bounded by the surface z=
5+(x-y)^2+2y and the planes x = 3, y = 3 and coordinate planes.
a. First, find the volume by actual calculation.
b. Estimate the volume by dividing the region into nine equal
squares and evaluating the functional value at the mid-point of the
respective squares and multiplying with the area and summing it.
Find the error from step a.
c. Then estimate the volume by dividing each sub-square above...

Calculate the volume bounded by the plane x + 2y + 3z = 6 by
coordinate planes with a triple integral.

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