Do examples as in the title exist? It depends on how the term Riemann sum is understood. For the standard, left, or right Riemann sums such examples do not exist. However, as we will see, they do ...

Implementations of the following numerical integration techniques are given below: Left-hand Riemann sum, Right-hand Riemann sum, Midpoint Rule, Trapezoid Rule, and Simpson's Rule. Modify and evaluate ...

To approximate the area under a graph we split the region up into many thin rectangles. Drag the slider labeled n to increase the number of rectangles used. The height of the approximating rectangle ...

Motivated by a proof without words for the sum of the alternating harmonic series, this article delves into some interesting questions regarding a series to which the usual convergence tests do not ...