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Ok, so first we need to find h(u).

By letting

h(u) = Integral -1 to 1 of (1/2)*g(u-x) dx

Then we can change the limits about by setting u = 2x

so now we have:

h(u) = Integral -2 to 2 of (1/4) du

so h(u) = 1

and I find the fourier transform of this between -2 and 2 and I don't get sin^2(k) / k^2

Can anyone help me here?

Thanks