AP Calculus BC : Numerical Approximations to Definite Integrals

Example Questions

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

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.

Explanation:

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

.

Explanation:

Explanation: