Active Calculus - Gvsu - Grand Valley State University

4.2. RIEMANN SUMS 97Activity 4.5.Suppose that an object moving along a straight line path has its position in feet at time t inseconds given by v(t) = 2 9 (t − 3)2 + 2.(a) Carefully sketch the region whose exact area will tell you the value of the distance theobject traveled on the time interval 2 ≤ t ≤ 5.(b) Estimate the distance traveled on [2, 5] by computing L 4 , R 4 , and M 4 .(c) Does averaging L 4 and R 4 result in the same value as M 4 ? If not, what do you think theaverage of L 4 and R 4 measures?(d) For this question, think about an arbitrary function f, rather than the particular functionv given above. If f is positive and increasing on [a, b], will L n over-estimate or underestimatethe exact area under f on [a, b]? Will R n over- or under-estimate the exact areaunder f on [a, b]? Explain.⊳