Question

Let E be the solid that lies between the cylinders x^2 + y^2 = 1 and x^2 + y^2 = 9, above the xy-plane, and below the plane z = y + 3.

Evaluate the following triple integral.

?x2 +y2? dV

Answer #1

1. Evaluate ???(triple integral) E
x + y dV
where E is the solid in the first octant that lies under the
paraboloid z−1+x2+y2 =0.
2.Evaluate ???(triple integral) square root ?x^2+y^2+z^2 dV
where E lies above the cone z = square root x^2+y^2 and between
the spheres x^2+y^2+z^2=1 and x^2+y^2+z^2=9

Let E be the solid that lies in the first octant, inside the
sphere x2 + y2 + z2 = 10. Express the volume of E as a triple
integral in cylindrical coordinates (r, θ, z), and also as a triple
integral in spherical coordinates (ρ, θ, φ). You do not need to
evaluate either integral; just set them up.

7. Given The triple integral E (x^2 + y^2 + z^2 ) dV where E is
bounded above by the sphere x 2 + y 2 + z 2 = 9 and below by the
cone z = √ x 2 + y 2 . i) Set up using spherical coordinates. ii)
Evaluate the integral

Find the volume of the solid that lies under the paraboloid z =
x^2 + y^2 , above the xy-plane and inside the cylinder x^2 + y^2 =
1.

Let S be the solid region in 3-space that lies above the surface
z = p x 2 + y 2 and below the plane z = 10. Set up an integral in
cylindrical coordinates for the volume of S. No evaluation

valuate SSSEz^2dV, where E is the solid region bounded below by
the cone z=2sqr(x^2+y^2) and above by plane z=10.
(SSS) = Triple Integral

Lets consider the solid bounded above a sphere x^2+y^2+z^2=2 and
below by the paraboloid z=x^2+y^2.
Express the volume of the solid as a triple integral in
cylindrical coordinates. (Please show all work clearly) Then
evaluate the triple integral.

Evaluate the triple integrals E y2 dV, where E is the solid
hemisphere x2 + y2 + z2 ≤ 9, y ≤ 0.
Calculus 3 Multivarible book James Stewart Calculus Early
Transcendentals 8th edition 15.8

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 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

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