Question 4. A heat conduction problem u(x, t) for a 5-meter length rod with the initial and boundary conditions is stated below. Find u(x, t) using separation of variables and the Fourier series. Vulxx = Ut u(x, 0) =x2 initial condition (t=0) u(0, t) = u(l, t) = 0 boundary conditions (x=0 and x= [) Hint: [ x2 sin(ax) dx = =x cos(ax) + 2 cos(ax) + 2xsin(ax) (20 marks)