In Exercises 1-6, find the integral, given that fo f(x) dx = 8, for (f(x))'dx = 12, f g(t) dt = 2, and fb (g(t))?dt = 3. 2 4. fo (f(x) ) da - (f. f(x) daIn Exercises 7-10, find the average value of the function over the given interval. 42. Let r(t) be the rate in meters / sec that water enters a reservoir at time t seconds. Given that J r(t) dt = 24, at what average rate does water enter or leave the reservoir on the interval 5 S t s 9?66. Using the graph of fin Figure 5.85, arrange the following quantities in increasing order, from least to greatest. i. So f(x) da ii. f? f(x) da iii. So f(x) da iv. S2 f(x) da v. - Si f(x) da vi. The number 0 vii. The number 20 viii. The number -10 10 f (x) X 2 3 -10 Figure 5.854. Let G'(t) = g(t) and G(0) = 4. Use Figure 6.12 to find the values of G(t) at t = 5, 10, 20, 25. g(1) 10 15 20 25 -2 Figure 6.12In Exercises 5-12, sketch two functions F such that F' = f. In one case let F(0) = 0 and in the other, let F(0) = 1.X f (x) 12. Problems 18-21 show the function f whose antiderivative F has F(0) = 0. Find the value of c that makes F(5) = 0. f (1) C 2 -16 18.28. Figure 6.17 shows the rate of change of the concentration of adrenaline, in micrograms per milliliter per minute, in a person's body. Sketch a graph of the concentration of adrenaline, in micrograms per milliliter, in the body as a function of time, in minutes. rate of change of adrenaline concentration (ug/ml/min) 1 (minutes) Figure 6.1739. The Quabbin Reservoir in the western part of Massachusetts provides most of Boston's water. The graph in Figure 6.23 represents the flow of water in and out of the Quabbin Reservoir throughout 2016. a. Sketch a graph of the quantity of water in the reservoir, as a function of time. b. When, in the course of 2016, was the quantity of water in the reservoir largest? Smallest? Mark and label these points on the graph you drew in part (a). > Answer c. When was the quantity of water increasing most rapidly? Decreasing most rapidly? Mark and label these times on both graphs. > Answer d. By July 2017 the quantity of water in the reservoir was about the same as in January 2016. Draw plausible graphs for the flow into and the flow out of the reservoir for the first half of 2017. rate of flow (millions of gallons/day) Outflow Inflow Jan (2016) April July Oct Jan (2017) Figure 6.234. Which of [I][V] are antiderivatives ofx] = I/X? I. In X II. 1/262 III. In X + 1n 3 IV. In [2X] V. In [X + 1]