General physics doubt

Somnath

Integration vs Summation   In above high school mathematics, integration and summation are often found in mathematical operations. They are seemingly used as different tools and in different situations, but they share a very close relationship. More about Summation Summation is the operation of adding a sequence of numbers and the operation is often denoted by the Greek letter of capital sigma Σ. It is used to abbreviate the summation and equal to the sum/total of the sequence. They are often used to represent the series, which essentially are infinite sequences summed up. They can also be used to indicate the sum of vectors, matrices, or polynomials. The summation is usually done for a range of values that can be represented by a general term, such as a series which has a common term. The starting point and the end point of the summation are known as the lower bound and upper bound of the summation, respectively. For example, the sum of the sequence a1, a2, a3, a4, …, an is a1 + a2 + a3 + … + an which can be easily represented using the summation notation as ∑ni=1 ai,  i is called the index of summation. More about Integration The integration is defined as the reverse process of differentiation. But in its geometric view it can also be considered as the area enclosed by the curve of the function and the axis. The value of the definite integral is actually the sum of the small strips inside the curve and the axis. The area of each strip is the height×width at the point on the axis considered. Width is a value we can choose, say ∆x. And height is approximately the value of the function at the considered point, say f(xi). From the diagram, it is evident that the smaller the strips are better the strips fit inside the bounded area, hence better approximation of the value. So, in general the definite integral I, between the points a and b (i.e in the interval [a,b] where a