(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

2. Relevant equations

[tex]\int\int_{S} dS[/tex]

3. 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?

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# Homework Help: Surface integral help.

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