My Math Forum Find area of surface x^2+y^2+z^2=4 which lies directly above cardioid p=1-cost

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 January 27th, 2015, 08:29 AM #1 Newbie   Joined: Jan 2015 From: USA Posts: 1 Thanks: 0 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!

 Tags area, cardioid, directly, find, lies, p1cost, surface, surface area, surfaceintegration, z24

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