Suppose a gauge at the outflow of a reservoir measures the flow rate of water in units of 6000- fts/hr. The total amount of water that flows out of the reservoir is the area under the flow rate curve. Consider the flow rate function shown in the figure to the right. Complete parts 4500- (a) through (d) below. Water flow rate (ft- / hr) 3000- 1500 10 Time (hr) a. Find the amount of water that flows out of the reservoir over the interval [0,3]. The amount of water that flows out of the reservoir over the interval [0,3] is (Simplify your answer. Type an integer or a decimal.) b. Find the amount of water that flows out of the reservoir over the interval [6, 10]. The amount of water that flows out of the reservoir over the interval [6, 10] is (Simplify your answer. Type an integer or a decimal.) c. Does more water flow out of the reservoir over the interval [0,3] or [3,5]? more water flows out of the reservoir over the interval (Simplify your answers. Type integers or decimals.) d. The units for the amount of water are the units of the water flow rate the time inThe following function is positive and negative on the given interval. f(x) =8 -2x2; [0,4] a. Sketch the function on the given interval. b. Approximate the net area bounded by the graph of f and the x-axis on the interval using a left, right, and midpoint Riemann sum with n = 4. c. Use the sketch in part (a) to show which intervals of [0,4] make positive and negative contributions to the net area. O A. O B. O C. OD. 18- Ay 18- 36- 12- 24- 12- 6- 24 12- 0- 12. X -6- X 6 -12- 0 6 8 -12- -12- -24- -181 -24J -36- b. The net area, approximated using the left Riemann sum, is The net area, approximated using the right Riemann sum, is The net area, approximated using the midpoint Riemann sum, is c. Which intervals of [0,4] make positive and negative contributions to the net area? Choose the correct answer below. O A. Positive contributions on [1,4]; negative contributions on [0, 1] O B. Positive contributions on [2,4]; negative contributions on [0,2] O C. Positive contributions on [0, 1]; negative contributions on [1,4] O D. Positive contributions on [0,2]; negative contributions on [2,4]Find the area of the following region bounded by the graph of f(x) = (x - 5)* and the x-axis between x = 4 and x = 6. The area is |units2. (Type an integer or a simplified fraction.)What is the average distance between the parabola y = 10x(18 - x) and the x-axis on the interval [0, 18]? The average distance is (Type an integer, proper fraction, or mixed number.)