534 B
534 B
Formal Definition
Let f be a continuous function on an interval [a, b].
Divide [a, b] into n equal parts of width \Delta x = \dfrac{b-a}{n}.
Let x_0, x_1, x_2, \cdots, x_n be the endpoints of this subdivision. x_0 = a and x_n = b.
Define \int_a^b f(x) dx = \lim_{n \to \infty} \sum_{i=1}^nf(x_i)\Delta x
\Delta xrefers to the width of each sub-intervalf(x_i)refers to the height of each subinterval.
Then let f be a continous function on [a, b] and let F be the any derivative of f (i.e )