Question

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

Answer #1

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.

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

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

consider the region E, which is under the surface z=8-(x^2+y^2) and
above the region R in the xy-plane bounded by x^2+y^2=4.
a) sketch the solid region E and the shadow it casts in the
xy-plane
b) find the mass of E if the density is given by
δ(x,y,z)=z

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

draw the solid bounded above z=9/2-x2-y2
and bounded below x+y+z=1. Find the volume of this
solid.

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...

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.

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.

find volume lies below surface
z=2x+y and above the region in xy plane bounded by x=0 ,y=1
and x=y^1/2

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