Question

Set up, but do not solve, the triple integral for determining the mass of the sphere ? = 10 sin? sin ? with a density of ?(?,?, ?) = ?.

Answer #1

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

Set
up BUT DO NOT SOLVE an integral or integrals that give the area
between the two loops of the curve r=3+6sin(θ)
plz answer ASAP

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.

Solve the triple integral where is the
unit ball

Let E be the solid that lies in the first octant, inside the
sphere x2 + y2 + z2 = 10. Express the volume of E as a triple
integral in cylindrical coordinates (r, θ, z), and also as a triple
integral in spherical coordinates (ρ, θ, φ). You do not need to
evaluate either integral; just set them up.

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

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

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.)

Set up an integral
that gives an average value x³ sin x
interval [-2, 1].

Sketch the graph. Set up (DO Not Evaluate) an integral for the
volume of the solid that results when the area bound by y=2x-x^2
and y= 0 is revolved about the y axis.

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