Question

the region enclosed by the cylinder x^2+y^2=64 and the planes z=0 and x+y+z=16

Answer #1

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Integrate f(x,y,z) = z over the region enclosed by x^2+y^2=2^2 ,
z=x^2+y^2 and z=0.

Integrate f(x,y,z) = z over the region enclosed by x^2+y^2=3^2 ,
z=x^2+y^2 and z=0.

Evaluate the surface integral (x+y+z)dS when S is part of the
half-cylinder x^2 +z^2=1, z≥0, that lies between the planes y=0 and
y=2

The volume of the object bounded by z = 0, z = x
planes and x = 2 -y * 2 parabolic cylinder is which of the
following?

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

Evaluate the flux, ∬SF⋅dS , of F(x,y,z)=yzj+z^2k through the
surface of the cylinder y^2+z^2=9 , z ≥ 0 , between the planes x=0
and x=3.

Let D be the solid in the first octant bounded by the planes
z=0,y=0, and y=x and the cylinder 4x2+z2=4.
Write the triple integral in all 6 ways.

Let D be the region enclosed by the cone z =x2 + y2 between the
planes z = 1 and z = 2.
(a) Sketch the region D.
(b) Set up a triple integral in spherical coordinates to ﬁnd the
volume of D.
(c) Evaluate the integral from part (b)

Verify the Divergence Theorem for the vector field F(x, y, z) =
< y, x , z^2 > on the region E bounded by the planes y + z =
2, z = 0 and the cylinder x^2 + y^2 = 1.
By Surface Integral:
By Triple Integral:

1. Find the area of the region enclosed between y=4sin(x) and
y=4cos(x) from x=0 to x=0.5π
2. Find the volume of the solid formed by rotating the region
enclosed by
x=0, x=1, y=0, y=8+x^5
about the x-axis.
3. Find the volume of the solid obtained by rotating the region
bounded by
y=x^2, y=1.
about the line y=7.

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