THE ANALYTICAL DEFINITION OF THE DEFINITE INTEGRAL: ANALYSIS

Fn = (x1 - x0) f(? 1) + (x2 - x1) f(? 2) +…+ (xn - xn-1) f(? n)

Fn = ?k(xk-1- xk) f(? k) = ?kf(? k) ? xk ,

where ? xk = (xk-1- xk)

f(x)dx = limn -->?Fn

THIS DEFINES THE AREA

UNDER THE CURVE IN THE

INTERVAL a < x < b

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