Edited.
I need to prove:
I(subscript 2k)=integral[-1,1](x^2k)*(cos(pi*x))dx
is equal to
I(subscript 2k)=-(4k/pi^2)-((2k)(2k-1)/(pi^2))*I(subscript 2k-2)
but i keep getting
I(subscript 2k)=-(4k/pi^2)+((2k)(2k-1)/(pi^2))*I(subscript 2k-2)
can anyone help?