Trapezoidal and Rectangular Integration, new post (con't from old)

Question

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))