Friday

July 25, 2014

July 25, 2014

Posted by **Johnnie** on Monday, March 10, 2014 at 10:22pm.

First time posting on this website, sorry for the lack of details on my attempts but I am really not sure where to start on this problem.

A formula that is useful is A(G)=∫∫√((f_x)^2+(f_y)^2+1)dA

*f_x is the partial derivative with respect to x, f_y is the partial derivative with respect to y

I know that I need to find an equation which should be x^2+y^2+z^2=a^2, and I need to find the limits which is where I am really struggling.

Also according to my professor, I shouldn't have to use any polar coordinate conversions in order to complete this problem, which was my initial approach.

- calculus -
**Steve**, Tuesday, March 11, 2014 at 12:06amThe circle in the x-y plane is

x^2 + (y - a/2)^2 = a^2/4

x^2 = a^2/4 - (4y^2-4ay+a^2)/4 = (y^2-ay)/4

The limits of integration in the x-y plane are

0 < y < a

0 < x < (1/2)√(y^2-ay)

then use symmetry and multiply by 4

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