Approximate the displacement of the object on this interval by sub dividing the interval into the indicated number of sub intervals.

Question

V= 9t+1(m/s),for 0 greater than or equal to t greater than or equal to 8; n =2

approximate displacement of object is ?

Answer 1

You didn't specify much about this but the displacement is the area under the line v(t) = 9t + 1 which can be estimate by rectangles however, you can see from the picture that neither the blue rectangles or the striped rectangles do a very good job of estimating the area. The area is actually a trapezoid so it can be measured accurately using the formula for the area of a trapezoid however the problem say "n = 2" which typically means to use two rectangles. I'll leave it to you to determine the base and height of each rectangle and add them up. A more accurate estimation would be to calculate the area of the blue rectangles then calculate the area of the striped rectangles and average the two areas. Or the best estimation would be to use the area of a trapezoid.