AP Calculus BC : Riemann Sum: Midpoint Evaluation

Study concepts, example questions & explanations for AP Calculus BC

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Example Questions

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Example Question #1 : Riemann Sum: Midpoint Evaluation

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 #2 : Riemann Sum: Midpoint Evaluation

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 #2 : Riemann Sum: Midpoint Evaluation

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 #3 : Riemann Sum: Midpoint Evaluation

Possible Answers:

Correct answer:

Explanation:

Example Question #5 : Riemann Sum: Midpoint Evaluation

Possible Answers:

Correct answer:

Explanation:

Example Question #6 : Riemann Sum: Midpoint Evaluation

Possible Answers:

Correct answer:

Explanation:

Example Question #7 : Riemann Sum: Midpoint Evaluation

Possible Answers:

Correct answer:

Explanation:

Example Question #8 : Riemann Sum: Midpoint Evaluation

Possible Answers:

Correct answer:

Explanation:

Example Question #9 : Riemann Sum: Midpoint Evaluation

Possible Answers:

Correct answer:

Explanation:

Example Question #4 : Riemann Sum: Midpoint Evaluation

Possible Answers:

Correct answer:

Explanation:

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