Trapezoidal and Rectangular Integration, new post (con't from old)
Rectangular Integration with Backward Differences:
If the width of a single sample is T, then the area of a rectangle at point n is T times xn. If writen
Yn = Yn-1 + T*Xn
then we can approximate y as a succession of rectangular areas like this
For trapezoidal integration divide the function into trapezoids spaced at the sample intervals. The area of a single trapezoid can be found by taking the average of the two ordinates and multiplying it by the width, T. The relevant equation is:
Yn = Yn-1 + T (( Xn + Xn-1) / (2))