Question

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.

Answer #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

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

Set up the triple integral, including limits, of the function
over the region.
f(x, y, z) = sin z, x ≥ 0, y ≥ 0, and below the plane 2x + 2y +
z = 2

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...

6. Let R be the tetrahedron in the first octant bounded by the
coordinate planes and the plane passing through (1, 0, 0), (0, 1,
0), and (0, 0, 2) with equation 2x + 2y + z = 2, as shown below.
Using rectangular coordinates, set up the triple integral to find
the volume of R in each of the two following variable orders, but
DO NOT EVALUATE.
(a) triple integral 1 dxdydz
(b) triple integral of 1 dzdydx

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).

Set up the integral. you do NOT have to
integrate.
A region is bounded by the x-axis and y = sinx with 0 ≤
x ≤ π. A solid of revolution is obtained by rotating that region
about the line y =−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.

57.
a. Use polar coordinates to compute the (double integral (sub
R)?? x dA, R x2 + y2) where R is the region in the first quadrant
between the circles x2 + y2 = 1 and x2 + y2 = 2.
b. Set up but do not evaluate a double integral for the mass of
the lamina D={(x,y):1≤x≤3, 1≤y≤x3} with density function ρ(x, y) =
1 + x2 + y2.
c. Compute??? the (triple integral of ez/ydV), where E=
{(x,y,z):...

when cylinder x^2+y^2=1, y^2+z^1=1 and x^2+z^1=1 intercept with
each other, set up a triple integral to calculate the volume of the
interception. (Dont have to evaluate the integral, but just set it
up.)

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