# What is the difference between summation and integration? [duplicate]

In high school we are studying Integral calculus

Before this we have studied summation which have symbol called 'sigma' $\sum$

Both works similar, sums up the numbers in domain

So my question is what is the difference between the two??

Because I am new to calculus, I don't know too much about calculus.

Please help!!

• See here and here. – user371838 Jan 28 '17 at 15:37
• Actually you can think of summation as integration with respect to the counting measure. – Thomas Jan 28 '17 at 15:41
• The differences are important, as noted, but you are right to notice the similarities. – Joffan Jan 28 '17 at 15:41

## 1 Answer

Summation is a discrete process where as integration is a continuous process.

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.

Another way to think of it is the summation is finding the area under the curve using rectangles of width $dx = 1$. Since the top of each rectangle can't match the angle of the curve, there is some area in the calculation that is actually above the curve. But the integral breaks the area into a nearly infinite number of rectangles, all with a width $dx$ approaching $0$.