F(t) is a periodic square wave function as shown. It takes only two values, 4 and 0, and stays at each of these values for 1 second before changing. What is the constant term in the Fourier series expansion of F(t)?

The Fourier series expansion of x³ in the interval −1 ≤ x < 1 with periodic continuation has

The Laplace Transform of $$f\left( t \right) = {e^{2t}}\sin \left( {5t} \right)\,u\left( t \right)$$ is

Laplace transform of $$\cos \left( {\omega t} \right)$$ is