Excel calculus

Definite Integration

b
∫f(t)dt = ∑ [((f(tp) - f(tp-1))/2)*(tp - tp-1)]
a

Here f(t) is the function which is to be integrated.
f(tp) is the value of the function at p-th cell in excel.
The summation is to be performed between a & b cells in excel.

There can be two errors due to assumption of the height of the rectangle as ((f(tp) - f(tp-1))/2) for area calculation. The other alternative heights can be f(tp) or f(tp-1). Error analysis shows that as the number of rectangles (smaller steps) or the number of cells increases, the value of percentage error decreases exponentially.

Example:

Plots of integration and error analysis of the function f(t) = t²





:-)