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Integrate problem

• To: mathgroup at smc.vnet.net
• Subject: [mg125959] Integrate problem
• From: Jing <jing.guo89 at yahoo.com>
• Date: Tue, 10 Apr 2012 02:26:25 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hello,

I am getting stuck when I try to integrate 2 expressions shown below:
1. g=1/4 (-Sqrt[3] x + y) Sqrt[r^2 - 1/4 (-Sqrt[3] x + y)^2];
2. f=r^2/2 ArcCos[(-Sqrt[3] x + y)/(2 r)];

x's limits is from -sqrt[r^2-y^2] to -y/sqrt[3]-1;
y's limits is from (-Sqrt[3] - Sqrt[12 r^2 - 9])/4 to (-Sqrt[3] + Sqrt[12 r^2 - 9])/4.
r is a variable and it is from sqrt[3]/2 to 1.

When I do the integrate on x, both of them can have result. After that, I try to do integrate on y, no results or some contain the imaginary part.

I am wondering that can someone help me to find the result?

Thanks a lot.

Jing