Question

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

Answer #1

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

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

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

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

Having trouble understanding.
(1 point) Evaluate the triple integral ∭E(xy)dV where E is the
solid tetrahedon with vertices
(0,0,0),(10,0,0),(0,6,0),(0,0,8).

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

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

Evaluate the triple integral _ D sqrt(x^2+y^2+z^2) dV, where D
is the solid region given by 1 (less than or equal to) x^2+y^2+z^2
(less than or equal to) 4.

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