### All AP Calculus BC Resources

## Example Questions

### Example Question #4 : Riemann Sums

Given a function , find the Right Riemann Sum of the function on the interval divided into four sub-intervals.

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In order to find the Riemann Sum of a given function, we need to approximate the area under the line or curve resulting from the function using rectangles spaced along equal sub-intervals of a given interval. Since we have an interval divided into sub-intervals, we'll be using rectangles with vertices at .

To approximate the area under the curve, we need to find the areas of each rectangle in the sub-intervals. We already know the width or base of each rectangle is because the rectangles are spaced unit apart. Since we're looking for the Right Riemann Sum of , we want to find the heights of each rectangle by taking the values of each rightmost function value on each sub-interval, as follows:

Putting it all together, the Right Riemann Sum is

.

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

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

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

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

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

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### Example Question #6 : Riemann Sum: Right Evaluation

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### Example Question #7 : Riemann Sum: Right Evaluation

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### Example Question #8 : Riemann Sum: Right Evaluation

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### Example Question #9 : Riemann Sum: Right Evaluation

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