Let f(x) be a continuous function on the interval [a, b]. Now divide the intervals [a, b] into n equal subintervals with each of width,

Δx = (b-a)/n, Such that a = x0 < x1< x2< x3<…..< xn = b

Then the Trapezoidal Rule formula for area approximating the definite integral

b∫a f(x)dx
is given by:
b∫a f(x)dx ≈
Where, xi = a+iΔx
If n →∞, R.H.S of the expression approaches the definite integral