# AP Calculus BC : Riemann Sum: Midpoint Evaluation

## Example Questions

### Example Question #1 : Riemann Sum: Midpoint Evaluation

Approximate

using the midpoint rule with . Round your answer to three decimal places.

Explanation:

The interval  is 4 units in width; the interval is divided evenly into four subintervals  units in width, with their midpoints shown:

The midpoint rule requires us to calculate:

where  and

Evaluate  for each of :

So

### Example Question #1 : Riemann Sum: Midpoint Evaluation

Approximate

using the midpoint rule with . Round your answer to three decimal places.

Cannot be determined

Explanation:

The interval  is 1 unit in width; the interval is divided evenly into five subintervals  units in width, with their midpoints shown:

The midpoint rule requires us to calculate:

where  and

Evaluate  for each of :

### Example Question #41 : Introduction To Integrals

Approximate

using the midpoint rule with . Round your answer to three decimal places.

None of the other choices are correct.

Explanation:

The interval  is  units in width; the interval is divided evenly into five subintervals  units in width, with their midpoints shown:

The midpoint rule requires us to calculate:

where  and

Evaluate  for each of :

Since ,

we can approximate  as

.

Explanation:

Explanation:

Explanation:

Explanation:

Explanation: