Applet: Area of Riemann sum
The area underneath the graph of $f(x)$ over the interval `{}` is calculated via a Riemann sum. The Riemann sum of `{}` subintervals is illustrated by the rectangles superimposed with the graph of $f$. As you move the pink point, a rectangle is highlighted; you can view the calculation of its area in the Details of one rectangle section. The calculation for the area over the whole interval `{}` is shown in the Area calculation section, along with the actual area calculated with a definite integral. You can switch between left and right Riemann sum using the slider; the function $f(x)$, the interval, and the number of rectangles can be changed via the Control panel section. The calculation yields the area under $f$ only for the case when $f(x) \ge 0$.
Applet file: area_riemann_sum.ggb
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