3.8 The Definite Integrals

Let \([a,b]\) be an interval on which a given function is continuous. Let \(x_0, x_1 , \cdots \cdots \cdots , x_n\) be points on the interval such that \(a = x_0 < x_1< x_2<\cdots \cdots \cdots < x_n = b\) and let
\(\Delta X_k = X_k - X_{k -1}\). Then the definite integral of \(f(x)\) with respect to \(X\) from \(X = a\) to \(X = b\) is given by \[\int ^b_a f(x) dx = \lim \limits _{n \rightarrow \infty } \sum ^n_{k = 1} f\big (X_k\big ) \hspace {0.1cm} \Delta X_k\]

Questions on this section

Stuck on something here? Ask below and it stays attached to this topic.