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