1. Find the average value of the function on the given interval. f(0) - sec 0 tan 0, [0, 7/4]. 2. Let f(x) = VI for z E [0, 4] a) Find c such that fave = f(c). b) Sketch the graph of f and a rectangle whose area is the same as the area under the graph of f 3. Prove that there exists ce [0, 4] such that for vie" dr - Vc fo er dr. 4. If f is continuous and f, f(x) dx - 8, show that f takes on the value 4 at least once on the interval [1, 3]. 5. Find the numbers b such that the average value of f(r) = 2 +6x - 312 On the interval [0, b] is equals to 3. 6. If fave[a, b] denotes the average value of f on the interval [a, b]. Show that for each c E [a, b] we have that favela, b] - " " favela, ] + " "favele, b ] 7. Consider the integral fo cos(r?) da. a) Find the approximations T4. Me and S, (Trapezoidal. Midpoint and Simpson's rule respectively) b) Estimate the errors involved in the approximations of (a)