- #1
Feodalherren
- 605
- 6
Homework Statement
Find the mass of [itex]z= \sqrt{x^{2}+y^{2}}[/itex] when 1 ≤ z ≤ 4.
The density function is ρ(x,y,z) = 10 - z
Homework Equations
The Attempt at a Solution
[itex]\int\int_{s} ρ dS[/itex]
[itex]S = <x, y, \sqrt{x^{2}+y^{2}} > [/itex]
therefore dS = [itex]< \frac{-x}{\sqrt{x^{2}+y^{2}}} , \frac{-y}{\sqrt{x^{2}+y^{2}}}, 1 >[/itex]
This is where I get sort of lost. Skipping a few steps I paramterized the function into polar coordinates and ended up with this integral
[itex]\int^{2pi}_{0}\int^{2}_{1} 10 \sqrt{1+r^2} - r\sqrt{1+r^2}drd\theta[/itex]
This just doesn't seem right, what am I missing?