Riemann Integral as a Special Case of Riemann-Stieltjes Integral
Keywords:
function, integration, integral, Riemann sum and Riemann-Stieltjes sumAbstract
In mathematics, integration (just the area of a region under the curve) is one of the most important areas and sciences
in general. In this article, some of the basic properties of Riemann and Riemann-Stieltjes integrals were briefly
reviewed. Definitions and relevant theorem were also investigated.Numerical techniques for the solution of both the
Riemann integral and the Riemann-Stieltjes integral were cited. Moreover, a theorem which gives full explanation on
how Riemann integral become a special case of Riemann-Stieltjes integral was boldly discussed. i.e Let A = ∫ f(x)dα(x)
b a be a Riemann-Stieltjes integrable. So, if α(x) = x, (an identity function).Then A = ∫ f(x)dx b a is Riemann
integrable.Therefore, this makes Riemann integral a special case of Riemann-Stieltjes integral and the integral may also differ.
