Question

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

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

write and evaluate the triple integral for the function f(x,y,z)
= z^2 bounded above by the half-sphere x^2+y^2+z^2=4 and below by
the disk x^2+y^4=4. Use spherical coordinates.

1.Set up the bounds for the following triple integral: R R R E
(2y)dV where E is bounded by the planes x = 0, y = 0, z = 0, and 3
= 4x + y + z. Do NOT integrate.
2.Set up the triple integral above as one of the other two types
of solids E.

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.

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.

2. Evaluate the double integral Z Z R e ^(x^ 2+y ^2) dA where R
is the semicircular region bounded by x ≥ 0 and x^2 + y^2 ≤ 4.
3. Find the volume of the region that is bounded above by the
sphere x^2 + y^2 + z^2 = 2 and below by the paraboloid z = x^2 +
y^2 .
4. Evaluate the integral Z Z R (12x^ 2 )(y^3) dA, where R is the
triangle with vertices...

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

The domain E of R^3 located inside the sphere x^2 + y^2 + z^2 =
12 and above half-cone z = sqrroot(( x^2 + y^2) / 3) (a) Represent
the domain E.
(b) Calculate the volume of solid E with a triple integral in
Cartesian coordinates.
(c) Recalculate the volume of solid E using the cylindrical
coordinates.

Evaluate Z Z Z E 20x 3 dV where E is the region bounded by x = 2
− y 2 − z 2 and x = 5y 2 + 5z 2 − 6.

Use a triple integral in cylindrical coordinates to find the
volume of the sphere x^2+ y^2+z^2=a^2

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