3. A uniform beam of length 4 units is governed by the boundary value problem Ely(4) (2) = f(2), y (0) = y' (0) =0, y' (4) = y" (4)=0 (a) If EI = = and f (x) = 2x, evaluate the deflection y (x) of the beam. (b) Find the Influence Function (Green's Function) G (x, 5) for the same beam. (c) Using your Influence Function, write the deflection y (x) of the same beam as a definite integral. (d) Hence, evaluate this integral. (e) Keeping EI = , suppose instead the applied load was f (x) = sin (x2). Why can't the deflection y (x) be evaluated directly in this case through direct integration? (f) Use your Influence Function from before to write the deflection y (x) of this beam as a definite integral. Do not attempt to evaluate the integral