Question

You want to estimate the area underneath the graph of a positive function by using four rectangles of equal width. The rectangles that must give the best estimate of this are those with height obtained from the:

1. Left endpoints
2. Midpoints
3. Right endpoints
4. This can’t be determined.

write down which option you think gives the best estimate.

Your statements can be about the velocity of the particle but could also be about its position or its acceleration.

Answer 1

Generally the best and closest approximation is given by the mid-points, since it will average out the values of left and right hand point, which will provide closer approximation.

For increasing function, left approximation will be lower than right one. For decreasing function, left approximation will be higher than the right one.

The mid-points generally provide the best approximate by averaging the value of left and right hand estimate in both types of function (i.e. increasing and decreasing)

Note - Post any doubts/queries in comments section.