- #1
TheSpaceGuy
- 25
- 0
Homework Statement
I have three problems and I could really use some help.
1. Integrate the function f(x,y,z) = y over the part of the elliptic cylinder
x^2/4 +y^2/9 = 1 that is contained in the sphere of radius 4 centered at the origin and such that x≥0, y≥ 0, z≥0.
2. Find the total mass of the half cylinder x^2+y^2 ≤ 9, x≥0, 0≤ z ≤ 2 with density p(x,y,z)= 9-x^2 -y^2 using cylindrical coordinates.
3. Use the spherical coordinates to integrate g(x,y,z) = sqrt(x^2 +y^2 +z^2) over the region x^2 +y^2 +z^3 ≤ 2z. Describe the region geometrically.
The Attempt at a Solution
Basically I just need help setting up the integrals for all of them. So If you can just do that, it would be great.
For the first problem I have so far
int(0 , 4) int(0 , sqrt (9-9x^2 / 4) ) int (0 , 1) y dzdydx
Is this right, and if not what is the correct integral.
For the second problem I have
int( 0 , pi) int(0 , 3) int(0 , 2) 9 - x^2 -y^2 r dzdrdθ
Is this right?
The third problem I have no idea what to do with it.
I know the procedure of spherical so please help me explaining to me how you got the correct integral. Thank you!