> N[2]:=x->4*(2-x)*(x-1); A[2]:=Diff(N[2](x),x)=diff(N[2](x),x);

                    N[2] := x -> 4 (2 - x) (x - 1)


                      d
              A[2] := -- (4 (2 - x) (x - 1)) = -8 x + 12
                      dx

> A[2]:=x->12-8*x;

                        A[2] := x -> 12 - 8 x

> F[2]:=Int((1-n^2+x^2)*N[2],x=1..2)=int((1-n^2+x^2)*N[2](x),x=1..2);

                      2
                     /                                    2
                    |         2    2                   2 n
           F[2] :=  |   (1 - n  + x ) N[2] dx = 11/5 - ----
                    |                                   3
                   /
                     1

> K[22]:=Int(x*(A[2]^2-(1-(n/x)^2)*N[2]^2),x=1..2)=int(x*(A[2](x)^2-(1-(
> n/x)^2)*N[2](x)^2),x=1..2);

              2
             /    /        /      2 \      \
            |     |    2   |     n  |     2|
  K[22] :=  |   x |A[2]  - |1 - ----| N[2] | dx =
            |     |        |      2 |      |
           /      \        \     x  /      /
             1

                   2       2
        36/5 - 44 n  + 64 n  ln(2)

> z[2]:=simplify((11/5-2*n^2/3)/(36/5-44*n^2+64*n^2*ln(2)));

                                              2
                                    -33 + 10 n
                z[2] := -1/12 -----------------------
                                      2       2
                              9 - 55 n  + 80 n  ln(2)

> z[2]:=evalf(subs(n=1,%));

                         z[2] := 0.2027837922

> y:=z+x=z[2]*N[2](x)+x;

            y := z + x = 0.8111351688 (2 - x) (x - 1) + x

> 
