3. Solve the initial value problem 12, y'(0) = 2, y(0) = 0 4. If the differentiable functions F(x) and G(x) both solve the initial value problem dy = f(x), y(To) = 90 on some interval I, must F(x) = G(x) for every a c /? Justify your answer. 5. What values of a and b minimize the value of / (x - 2x? )dx? 6. Combine the direct definition of integral with your elementary geometry skills to evaluate ( 2 ) [ (2 - 120)da (b) (1 - VI-12) do 7. Show that / sinaldr * 2 8. The average value of an integrable function f : [a, b] -> R is defined as av (f ) = a's / f(x)de. Determine whether the following rules hold. If yes, prove. If not, give a counterexample to disprove