> W(xi) := (1-xi)*xi;

                         W(xi) := (1 - xi) xi

> R(xi) :=1-
> 4*C[1]+2*C[1]*xi-2*C[1]^2*(1-xi)*xi+C[1]*(C[1]*(1-2*xi)-2)*(1-2*xi);

                                          2
  R(xi) := 1 - 4 C[1] + 2 C[1] xi - 2 C[1]  (1 - xi) xi

         + C[1] (C[1] (1 - 2 xi) - 2) (1 - 2 xi)

> Int(W*R,xi=0..1)=int(W(xi)*R(xi),xi=0..1);

                1
               /
              |                       2
              |   W R dxi = -1/30 C[1]  - 1/2 C[1] + 1/6
              |
             /
               0

> evalf(solve(1/6-(1/2)*C[1]-C[1]^2/30=0,C[1]));

                      -15.32623792, 0.326237920

> 
