Improper Integrals and Applications of Riemann Integrals

Abstract

So far, our theory of integration has dealt with the definite integral

$${\int \nolimits \nolimits }_{a}^{b}f(x)\,\mathrm{d}x,$$

where the integrand f(x) is bounded on a closed and bounded interval [a, b]. Thus, definite integrals have finite limits of integration, and f(x) has a finite range.