Question

A solid E lies within the cylinder x^2+y^2=1, below the plane z=4, and above the paraboloid z=2-x^2-y^2. The density of the solid is p(x,y,z)=sqrt(x^2+y^2). Calculate the mass of the solid.

Answer 1

hmmm, debating between a triple integral and a double integral

Answer 2

i'm going with the triple integral
since it's finding a mass

Answer 3

you have a graphing software?

Answer 4

nope. I have the answer just not the work behind it.
Im taking myself through some triple integral reviews to see if i can figure out how to do it.

Answer 5

let me graph this thing first

Answer 6

oh, this is fairly simple

Answer 7

it will be tripleintegral(sqrt(x^2+y^2))dzdydx
the limits for dz is from z=2-x^2-y^2 to z=4
the limits for dy is from y=-sqrt(1-x^2) to y=sqrt(1-x^2)
the limit for dx is from x=-1 to x=1

Answer 8

this is the picture of z=2-x^2+y^2

Answer 9

That makes more sense. I think i should do some more examples before my final though lol.