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January 27th, 2015, 08:29 AM   #1
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Find area of surface x^2+y^2+z^2=4 which lies directly above cardioid p=1-cost

The formula for the surface area seems to be obvious using polar coordinates:
$\displaystyle S=∫_0^π▒∫_0^(1-cosθ)▒2/√(4-ρ^2 ) ρdρdθ$ but then I get stuck on solving the integral:

$\displaystyle 4∫_0^π▒√(4-〖(1-cosθ)〗^2 ) dθ$

I tried various substitution methods but still couldn't find the right solution.

Any hint/help would be greatly appreciated.

Thanks!
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area, cardioid, directly, find, lies, p1cost, surface, surface area, surfaceintegration, z24



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