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Your task is to estimate how far an object traveled during the time interval 0 t 8 but you only have the following data about the velocity of the object Time seconds 0 Velocity feet per second 1 Q J To 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 like the black curve in the graph below 3 1 2 3 1 1 Total distance Total displacement 4 5 6 7 8 4 1 4 3 2 7 8 You decide to use a left endpoint Riemann sum to estimate the total displacement So you pick up a blue pen and draw rectangles whose height is determined by the velocity measurement at the left endpoint of each one second interval By using the left endpoint Riemann sum as an approximation you are assuming that the actual velocity is approximately constant on each one second interval or equivalently that the actual acceleration is approximately zero on each one second interval and that the velocity and acceleration have discontinuous jumps every second This assumption is probably incorrect because it is likely that the velocity and acceleration change continuously over time However you decide to use this approximation anyway since it seems like a reasonable approximation to the actual velocity given the limited amount of data A Using the left endpoint Riemann sum find approximately how far the object traveled

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