Calculus 2 : Riemann Sums

Study concepts, example questions & explanations for Calculus 2

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Example Questions

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Example Question #91 : Riemann Sums

Possible Answers:

Correct answer:

Explanation:

Example Question #92 : Riemann Sums

Compute the following integral by using four equal left hand Riemann sums:

Possible Answers:

Correct answer:

Explanation:

Riemann sums are simply estimating the area under the curve of our function using an approximation of a rectangle.  The area of a rectangle is given by .  Therefore, we need to figure both of these values for our four boxes and sum them all up.  Since the boxes are equal, we can simply find the width by the following equation:

 and  are your integration limits, and  refers to the number of boxes.

The length of all of our boxes is given by the function.  Since, this is a left Riemann sums, we need to consider the left side of each integration interval. 

For the lengths, we used -values of , since those are the starting points of our four intervals. 

Example Question #93 : Riemann Sums

Approximate the following integral with four equal right Riemann sums:

Possible Answers:

Correct answer:

Explanation:

Riemann sums are simply estimating the area under the curve of our function using an approximation of a rectangle.  The area of a rectangle is given by .  Therefore, we need to figure both of these values for our four boxes and sum them all up.  Since the boxes are equal, we can simply find the width by the following equation:

 and  are your integration limits, and  refers to the number of boxes.

The length of all of our boxes is given by the function.  Since, this is a right Riemann sums, we need to consider the right side of each integration interval. 

For the lengths, we used -values of , since those are the ending points of our four intervals. 

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