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1. HOMEWORK (1) Calculate the average value of f (:3) = 1:10 on [0, 1]. (2) Calculate the average value of f (t) = 2' on (a) [3,4]. (b) [3,31]. (c) [3,301]. (d) [3,3001]. (3) The table gives values of a temperature T(t) of an object at time t. Using the Midpoint Rule estimate the average value of T on [0,30]. (4) Calculate the average value of f(t) = sint on (a) the interval [0, 7r]. (b) on the interval [0, 1:]. (c) Show that as a: > 00, lm] > 0. (5) Let f,,(a:) = cos(mc). Graph f9. Guess an antiderivative of f,,(zc) with respect to :5 and check your guess by differentiating. Then calculate Em] and show that 31%: am,\" =