# Area under the Exponential Curve

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Consider a curve consisting of segments joining the points , where and . The region under this curve is broken into triangular pieces by extending the segments to the axis. Each extended segment projects onto a segment of length 1 on the axis because .

[more]

You can align these triangles one on top of the other above the interval [0,1] on the axis using the "align" slider. You can control the constant using the "triangles per unit length" slider.

Let . As and tend to infinity, the curve approaches the exponential curve . The "total length" slider controls the length of the interval. As the total length tends to infinity, the aligned triangles fill the unit square of area 1.

[less]

Contributed by: Okay Arik (March 2011)
Open content licensed under CC BY-NC-SA