Question

point) Your task is to estimate how far an object traveled during the time interval 0 S t S 8, but you only have the following data about the velocity of the object. time (sec) 01 2 3 4 5678 velocity feet/sec)-24-3-4-2-3231 get an idea of what the velocity function might look like, you pick up a black pen, plot the data points, and connect them by curves. Your sketch looks something e the black curve in the graph below. 1,8 Left endpoint approximation A) Using the left endpoint Riemann sum, find approximately how far the object traveled. Your answers must include the correct units Total displacement Total distance traveled In the following scenario, we consider the distribution of a quantity along an axis Suppose that the function c(r) 200+100e0.1*models the density o traffic on a straight road, measured in cars per mile, where x is number of miles east of a major interchange, and consider the definite integral 200 + 100e-0.13dx. -0.1x (i) What are the units on the product c(x)-△x? Units: cars (ii) What are the units on the definite integral and its Riemann sum approximation given by Units: cars (i) Evaluate the definite integral o cx) dx -Jo (200+100e-0.1') dx and write one sentence to explain the meaning of the value you find. 581.269; Scenario B In the following scenario, we consider the distribution of a quantity along an axis On a 6 foot long shelf filled with books, the function B models the distribution of the weight of the books, measured in pounds per inch, where x is the number of inches from the left end of the bookshelf. Let B(r) be given by the rule B(x 0.5+ (i) What are the units on the product B(x)-/>x? Units: pounds (i) What are the units on the definite integral and its Riemann sum approximation given by 36 12 Units: pounds 72 72 ii) Evaluate the definite integralB(x) dx- (0.5+ ) dx and write one sentence to explain the meaning of the value you find. J0 36.986

Answer 1