1. The problem statement, all variables and given/known data By applying Parseval's (Plancherel's) theorem to the function are given by: f(x) = -1 for -2 ≤ x < 0 1 for 0 ≥ x < 2 0 otherwise determine the value of the following integral. ∫ dk sin^4(k)/(k^2) (Integral between ±infinity) 2. Relevant equations Parseval's Theorem, i.e the integral of the modulus squared of a function is equal to the integral of the modulus squared of its fourier transform. Fourier Transform formula. 3. The attempt at a solution I've tried multiple times to try and arrive at the correct answer of pi/2 but I just can't do it. Is the fourier transform: ∫-dx e^(ikx) + ∫ dx e^(ikx)? (First integral is between -2 and 0, second between 0 and 2). Because I can't get the correct answer doing that. And for the equation of the function, is it just sgn(x), with the integral between -2 and 2? How else do I write f(x) given those boundaries? If I use sgn(x) between -2 and 2, I get 4 for the left hand side. But I still can't derive that integral. If someone would just start me off with the correct fourier transform equation, i'll go away and crunch the integration myself. Thank you.