Question

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

Answer #1

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

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

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

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

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.

Evaluate the triple integral.
2 sin (2xy2z3) dV, where
B
B =
(x, y, z) | 0 ≤ x ≤ 4, 0 ≤ y ≤ 2, 0 ≤ z ≤ 1

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).

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

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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