Area under the exponential curve

Area, Calculus, Curves and Exponential FunctionsConsider a curve consisting of segments joining the points(n/k,an), where an=(1-1/k)^n and n=1,2,3,... . The region under this curve is broken into triangular pieces by extending the segments to the x axis. Each extended segment projects onto a segment of length 1 on the x axis because an/(k(an-an+1))=1 You can align these triangles one on top of the other above the interval [0,1] on the x axis using the "align" slider. You can control the constant using the "triangles per unit length" slider. Let x=n/k. As n and k tend to infinity, the curve approaches the exponential curve y=e^(-x). The "total length" slider controls the length of the x interval. As the total length tends to infinity, the aligned triangles fill the unit square of area 1Componente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic