Question

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.

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

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

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 D be the solid region defined by D = {(x, y, z) ∈ R3; y^2 +
z^2 + x^2 <= 1},
and V be the vector field in R3 defined by: V(x, y, z) = (y^2z +
2z^2y)i + (x^3 − 5^z)j + (z^3 + z) k.
1. Find I = (Triple integral) (3z^2 + 1)dxdydz.
2. Calculate double integral V · ndS, where n is pointing
outward the border surface of V .

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).

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...

Set up, but do not evaluate, an integral of f(x,y,z) = 20−z over
the solid region deﬁned by
x^2 +y^2 +z^2 ≤ 25 and z ≥ 3. Write the iterated integral(s) to
evaluate this in a coordinate system of your choosing, including
the integrand, order of integration, and bounds on the
integrals.

Find the volume of the solid using triple integrals. The solid
region Q cut from the sphere x^2+y^2+z^2=4 by the cylinder r=2sinϑ.
Find and sketch the solid and the region of integration R. Setup
the triple integral in Cartesian coordinates. Setup the triple
integral in Spherical coordinates. Setup the triple integral in
Cylindrical coordinates. Evaluate the iterated integral

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 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.

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