# numerically solving linear integral equations

I want to solve a 3*3 linear equation system but the equations are integral equations and he coefficients of solutions are to be extracted NUMERICALLY from some other integrals.I do not know how. I can locate the coefficients into the Ax = b system if I can extract the coefficients numerically... For example, I have 3 unknowns(h, theta, c), 4 integrals :

 u1 (x)= 1/(1-sin(pi*x) )*[-4*int_0^x [h+theta(x-0.5)]dx +c]
u2 (x)= 1/(1-sin(pi*x) )*[-4*int_0^x [-h-theta(x-0.5)]dx -c]
p1 (x)= 3* int_0^x [u1(x)]dx
p2 (x)= 3* int_0^x [u2(x)]dx


So I want to extract the coefficients of h, theta, and c from above integrals and below integrals and solve a Ax = b system. I have this below integral equations:

Equation1) 3* int_0^1 [u2(x)-u1(x)] dx = beta
Equation2) int_0^1 [p2(x)-p1(x)] dx = 12 *h
Equation3) int_0^1 [(x-0.5) p2(x)-p1(x)]dx = 12 *h


I need to find h,theta, c.