Mathematical Regime

Riemann sums and Integral was introduced by a German Mathematician Bernhard Riemann . What are Riemann sums?  How do you convert integrals to Riemann sums?  How do you calculate Riemann integral ?  Its argument arose when we want to find the area under the curve of a function. Imagine that you are given a rectangle or any other polygon or a function how will you calculate the area under the curve ?    Riemann sums (RS) is there to help you. I t is used to approximate the area under the curve of a function by adding shapes like rectangle, trapezoid, etc . But the question here is how can we make these rectangles? There are three choices when it comes to making rectangles to approximate the area.

What is the concept of integration ?  What is the purpose of integration ?  Why does integrating give you area under the curve? Integration, also known as  anti-derivative   of a function, gives the area under the curve of the function.  Most of you already know all this thing but did  you  ever wonder  why integration gives you area under the curve?  How does it work actually? Well, the answer is quite simple and basic. We will take some polynomials as examples and the integration rule for a polynomial term of an arbitrary degree n " $ax^n $  " is given by \[\int ax^n dx=\frac{ax^{n+1}}{n+1}+C\]