Left, Right, Midpoint Riemann Sums
Adapted from J Mulholland and Gary Rubinstein's Riemann Sums Activity.
The area under a graph between x = a and x = b can be approximated by partitioning the region into n rectangles with uniform width equal to Δx = (b - a)/n (the length of the input interval divided by the number of rectangles used to approximate the area). Drag the slider labeled n to increase the number of rectangles used. Drag the points labeled a and b to change the endpoints of the region.
The height of each approximating rectangle can be defined using the output at the top-left corner, the output at the top-right corner, or the value of the function at the midpoint of its base. Drag the slider labeled "position" to change the point used for the height of the rectangle.
The sum of the areas of all the thin rectangles is the Riemann Sum displayed. Click the "actual area" button to compare the approximation to the true value of the area under the graph.
To change the function f, say to sin(x), then just type f(x) = sin(x) in the input field at the bottom of the applet.