1. The graph below represents the velocity (in meters/sec) of an object moving along a straight-line path that runs from west to east, with east being considered the positive direction. Assume the object's initial position is s(0) = 0. (a) What is the total distance the object has traveled over the time interval [0,9]? Show your work. (b) What is the total change in position on the time interval [0,9]? Show your work. 2. The graph of f(x) = x3 4x is given below. We are interested in the left Riemann sum over the interval [1,2] with 6 subintervals. (a) On the above graph, clearly draw and shade the rectangles associated with L, on [1,2]. Make sure you clearly mark the appropriate values on the x-axis and state the value of Ax. (b) What does Lg represent? You CANNOT tell me it is the left Riemann sum over the interval [1,2] with 6 subintervals. I already know that. You need to tell me what this Riemann sum represents (i.e., what are you actually computing when you are computing Lg). You must be very specific. Refer to your work in part (a) to answer this question. (c) SET UP the computation of Lg on [1,2] by hand. Show the complete set-up of what you are adding up. Show all work clearly. Your final answer should be an expression of numbers. It would be the last step before you would punch into a calculator. You do NOT NEED to add by hand. 3. The graph of y = f (x) is given below. Find the value of each of the following integrals. SHOW ALL WORK. Answers without full work will not receive any credit. V (a) Sof(x) dx 2 8 10 12 (b) Sof (x) dx -2- -4 (c) So f(x) dx (d) S 2f(x) dx4. (a) Find the average value of f(x) = 3 x over the interval [0,2]. SHOW ALL WORK. (b) Find the value(s) of x at which the value of the function is equal to the average value over the interval [0,2]. SHOW ALL WORK. (c) What do your answers from part (a) and (b) represent graphically? The graph of f(x) =3 x is given below for your convenience. Make sure you clearly explain your answer. Hint: You will need to sketch something on this graph AND then tell me something about what you sketched