Streifenmethode des archimedes biography

Archimedes’ method

Archimedes of Syracus lived 287 to 212 B.C. and was one of the most important mathematicians of his time. He found a method to calculate the exact area under the curve of a parabola.

It was not until 1630 when Cavalieri continued work in this area of mathematics, followed by Newton and Leibniz around 1670 who developed calculus. The “strip method”, Archimedes uses, is fundamental for understanding the ideas involved in integration.

Find an estimate of the area between the graph of the function and the x-axis.

Here, the interval is divided into 4 equal strips.

Streifenmethode des archimedes biography

In the first diagram, the height is always equal to the lowest value of f(x) in that interval while in the second diagram the height is equal to the maximum value of f(x) in that interval. These are the lower sum (inferior Riemann sum) and the upper sum (superior Riemann sum), respectively (Ger.

Untersumme und Obersumme).

Task 1

Calculate the lower sum are