Question

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

Answer #1

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 (6 − x^2 − y^2) dV, where H
is the solid hemisphere x^2 + y^2 + z^2 ≤ 16, z ≥ 0.

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

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 cylindrical coordinates.
Evaluate
x2 + y2
dV,
E
where E is the region that lies inside the cylinder
x2 + y2 = 25 and between
the planes
z = −4
and
z = −1.

Use spherical coordinates.
I=exp[-(x2+y2+z2)3/2;
E=upper hemisphere of radius 2

Evaluate ∫∫Sf(x,y,z)dS , where f(x,y,z)=0.4sqrt(x2+y2+z2)) and S
is the hemisphere x2+y2+z2=36,z≥0

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.

Use spherical coordinates.
(a) Find the centroid of a solid homogeneous hemisphere of
radius 1. (Assume the upper hemisphere of a sphere centered at the
origin. Use the density function
ρ(x, y,
z) = K.
(x, y, z) =
(b) Find the moment of inertia of the solid in part (a) about a
diameter of its base.
Id =

Let H be the hemisphere x2 + y2 + z2 = 54, z ≥ 0, and suppose f
is a continuous function with f(2, 5, 5) = 9, f(2, −5, 5) = 11,
f(−2, 5, 5) = 12, and f(−2, −5, 5) = 13. By dividing H into four
patches, estimate the value below. (Round your answer to the
nearest whole number.)
H
f(x, y, z) dS

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