Calculus :

11. I just need the final answer. I have tried 19.36 and 20.17

1. [ODS/0.25 Points] DETAILS PREVIOUS ANSWERS SESSCALCZ 4.2.010. 9 The table gives the values of a function obtained from an experiment. Use them to estimate / f(x) dx using three equal subintervals with right endpoints, left endpoints, and midpoints. 3 X 3 4 5 6 l 7 8 9 f(X) 3.3 2.3 0.5 0.3|0.9 1.5 1.8 9 (a) Estimate / f(x) dx using three equal subintervals with right endpoints. 3 R3: If the function is known to be an increasing function, can you say whether your estimate is less than or greater than the exact value of the integral? ' less than 0 greater than one cannot say ~J/ 9 (b) Estimate / f(x) dx using three equal subintervals with left endpoints. 3 L3: If the function is known to be an increasing function, can you say whether your estimate is less than or greater than the exact value of the integral? 0 less than ' greater than one cannot say \\J/ 9 (c) Estimate / f(x) dx using three equal subintervals with midpoints. 3 M3: If the function is known to be an increasing function, can you say whether your estimate is less than or greater than the exact value of the integral? less than ' greater than 0 one cannot say \\J/ EXAMPLE 7 A particle moves along a line so that its velocity at time t is v(t) = t - t - 20 (measured in meters per second). (a) Find the displacement of the particle during 3 s t s 6. (b) Find the distance traveled during this time period. SOLUTION (a) By this equation, the displacement is s ( 6) - 5(3 ) = vit ) at (2 - t - 20 ) dt 76 t2 - 20t N -10.5 This means that the particle's position at time t = 6 is 10.50 meters to the left of its position at the start of the time period. (b) Note that v(t) = t2 - t - 20 = (t - 5)(t + 4) and so v(t) s @ . 0 on the interval [3, 5] and v(t) >