- #1
Johnny Blade
- 30
- 0
Homework Statement
What is the area of the portion of the sphere [tex]x^{2}+y^{2}+(z-a)^{2}=a^{2}[/tex] that is inside the paraboloid [tex]z=x^{2}+y^{2}[/tex]
Homework Equations
[tex]\int\int_{S} dS[/tex]
The Attempt at a Solution
I used this
[tex]\int\int_{S} dS=\int\int_{R}\sqrt{f^{2}_{x}+f^{2}_{y}+1}dx dy[/tex]
And got
[tex]=\int\int_{R}\frac{a}{\sqrt{a^{2}-x^{2}-y^{2}}}dx dy[/tex]
I know that R is the projection of the surface on the xy plane, but I tried a few different ways to compute the boundaries but it never made sense. Maybe I'm just approaching it the wrong way. Anyone can help me with this?