# AP Calculus BC : Riemann Sum: Midpoint Evaluation

## Example Questions

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### Example Question #29 : Integrals

Approximate

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

Possible Answers:

Correct answer:

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 #30 : Integrals

Approximate

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

Possible Answers:

Cannot be determined

Correct answer:

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 #31 : Integrals

Approximate

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

Possible Answers:

None of the other choices are correct.

Correct answer:

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

.

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

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Correct answer:

Explanation:

### Example Question #2 : Riemann Sum: Midpoint Evaluation

Possible Answers:

Correct answer:

Explanation:

### Example Question #34 : Integrals

Possible Answers:

Correct answer:

Explanation:

### Example Question #3 : Riemann Sum: Midpoint Evaluation

Possible Answers:

Correct answer:

Explanation:

### Example Question #36 : Integrals

Possible Answers:

Correct answer:

Explanation:

### Example Question #4 : Riemann Sum: Midpoint Evaluation

Possible Answers:

Correct answer:

Explanation:

### Example Question #5 : Riemann Sum: Midpoint Evaluation

Possible Answers:

Correct answer:

Explanation:

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