All AP Calculus BC Resources
Example Questions
Example Question #11 : Riemann Sum: Left Evaluation
Example Question #12 : Riemann Sum: Left Evaluation
Example Question #13 : Riemann Sum: Left Evaluation
Example Question #14 : Riemann Sum: Left Evaluation
Example Question #15 : Riemann Sum: Left Evaluation
Example Question #1 : Riemann Sum: Right Evaluation
Given a function , find the Right Riemann Sum of the function on the interval divided into four sub-intervals.
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
.