You are given the following information about functions f and g: Information about f: . fif ( x ) dx = 7 . JA f ( x ) dx = - 3 Information about g: . fig ( x ) dx = -2 . 1 8 (x ) dx = 5 Find the exact value of each of the following expressions. a) / (f ( x ) - 38 (x) ) dx = (Enter a numeral) b) / ( f ( x ) + 3 ) dx = (Enter a numeral) c) (3g(x)) dx = (Enter a numeral)The figure below shows the graph of a function f on the interval [a, c]. If the areas of the regions bounded by the graph and the horizontal axis are as shown, then find each of the following values. f(m) Area = 13 a a) / f(x) dx = (Enter a numeral) b C b) / f(x) dx = 11 (Enter a numeral) 11 c) The total shaded area = (Enter a numeral) '8. WI; 0'0 W T a l [11 a I I I I 7'7 '5' I I I I I I I I I I I '7" C a" '7 a a A car is traveling in a straight line with a velocity of 85 feet per second when the driver applies the brakes. The car's velocity then decreases continuously over a period of 10 seconds until the car stops. The car's velocity is measured every 2 seconds while it is braking, and these values are given in the table below. n--nn- mm a) Use a right-hand Riemann sum to estimate the car's total stopping distance over the 10-second period, using n = 5 rectangles. Total stopping distance a: |:| :| (Enter a numeral in the blank and select the correct units from the pull-down menu) b) Assume that the car's velocity is continuous and decreasing over the entire 10 second period. What, if anything, can you conclude about the righthand Riemann sum estimate from part a), of the car's total stopping distance? The right-hand Riemann sum underestimates the stopping distance. There is not enough information to draw a conclusion. The righthand Riemann sum overestimates the stopping distance. ' The righthand Riemann sum gives the exact stopping distance. mmua-nua-... ak-.7..- n. ..-:-....= _.- n WNW MO? .> "/1? .-- .I _ _ 5% l l '33 u u l u I u u u u u . Use Riemann sums to approximate the following integral to at least 3 decimal places using n = 24 rectangles. You may use the Desmos Riemann sum calculator or the TI84 emulator. Use the indicated Riemann sums, not the Fundamental Theorem! 1 / (14 x2) dx 3 Lefthand Riemann sum: L24 = (Enter a decimal number accurate to at least 3 decimal Right-hand Riemann sum: R24 = (Enter a decimal number accurate to at least 3 decimal Suppose that money flows into a vending machine at the rate of R(2') dollars per day, where time t is measured in days. The vending machine's income rate for a particular 30- day period was tabulated, and the results are shown below. x; "7-7 n @ S g in?9 g '> ii/ L? a ['l a I I I I ".' 1" I I I I I I The graph of the function g is shown below. Use the graph to find the value of each expression. y = g(x) 3 2 X . -1 0 1 2 3 4 5 6 -1 -2 -3 al / g(x) dx = (Enter a numeral) b) Find the average value of g on the interval [0, 6]. Round your answer to at least 2 decimal places. NA4 y = g(x) W N 0 1 2 3 4 5 6 -1 -2 -3 2) / g(x) dx = (Enter a numeral) b) Find the average value of g on the interval [0, 6]. Round your answer to at least 2 decimal places. gAVG[a, b] = (Enter a decimal number accurate to at least 2 decimal places)