Question

Use cylindrical coordinates.

Evaluate

dV, |
|||

E |

where *E* is the region that lies inside the cylinder
*x ^{2}* +

* z* = −4

and

* z* = −1.

Answer #1

Use spherical coordinates.
Evaluate
(x2 + y2) dV
E
,
where E lies between the spheres
x2 + y2 + z2 = 9 and
x2 + y2 + z2 = 16

Use cylindrical coordinates.
Evaluate
6(x3 + xy2) dV, where E is
the solid in the first octant that lies beneath
the paraboloid z = 4 − x2 − y2.
E

Use cylindrical coordinates.
Evaluate the integral, where E is enclosed by the
paraboloid
z = 8 + x2 + y2,
the cylinder
x2 + y2 = 8,
and the xy-plane.
ez dV
E

Use cylindrical coordinates.
Evaluate the integral, where E is enclosed by the
paraboloid
z = 7 + x2 + y2,
the cylinder
x2 + y2 = 8,
and the xy-plane.
ez dV
E

Use spherical coordinates. Evaluate (2 − x2 − y2) dV, where H is
the solid hemisphere x2 + y2 + z2 ≤ 25, z ≥ 0. H

Use spherical coordinates.
Evaluate
(2 − x2 − y2) dV, where H is
the solid hemisphere x2 + y2 + z2
≤ 25, z ≥ 0.
H

Use spherical coordinates.
Evaluate
xyz
dV
E
,
where E lies between the spheres ρ = 2 and
ρ = 5 and above the cone ϕ = π/3.

Evaluate the double integral ∬Ry2x2+y2dA, where R is the region
that lies between the circles x2+y2=9 and x2+y2=64, by changing to
polar coordinates .

Evaluate the double integral ∬Ry2x2+y2dA,∬Ry2x2+y2dA,
where RR is the region that lies between the circles
x2+y2=16x2+y2=16 and x2+y2=100,x2+y2=100, by changing to polar
coordinates.

Use spherical coordinates to evaluate the following integral, ∫
∫ ∫ y2z dV, E where E lies above the cone φ = π 4 and below the
sphere ρ = 9

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