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Estimating Area with Finite Sums
8. Definite Integrals / Estimating Area with Finite Sums / Problem 4
Problem 4

A car traveling along a straight road has a velocity in m/s\(\text{m}\)/\(\text{s}\) represented by the graph of v=f(t) v = f(t) on the interval 0t12 0 \(\leq\) t \(\leq\) 12 , as shown. The time tt is in seconds. Divide [0,12][0,12] into n=2 n = 2 subintervals: [0,6][0,6] and [6,12][6,12]. Estimate the displacement of the car on [0,12][0,12] by assuming that the car travels at a constant velocity equal to the value of v v evaluated at the midpoint of each subinterval.
Graph showing velocity v=f(t) over time t, with shaded areas representing displacement estimates for subintervals.