Find the Fourier transform off (t) ={ 1, |t| < 1;0, |t| > 1.Hence evaluate the integral ∫ ∞0 sin tt dt.Solution: F(ω) = 2 sin ωω ,∫ ∞0sin tt dt = π2 .2. Find the Fourier sine and cosine transform of f (t) = e−at, a > 0.Solution: Fs(ω) = ωω2 + a2 , Fc(ω) = aω2 + a2 .3. Find the Fourier transform off (t) =−(1 + t), −1 ≤ t ≤ 0;t − 1, 0 < t ≤ 1;0, |t| > 1.Solution: F(ω) = 2(cos ω − 1)ω2 .4. Find the inverse Fourier transform ofF(ω) = e−iω2(1 + iω) .Solution: f (t) = 12 e−(t−1) H(t − 1), where H is the Heaviside step function.5. Find the Fourier transform off (t) ={ cos t, −l ≤ t ≤ l;0, |t| > l.Solution: F(ω) = 2ω cos l sin ωl − sin l cos ωlω2 − 1 .