Difference between summation and integration [closed]

I understand calculus and maths but when i apply statistics and add up numbers they both look kinda same

Can anybody explain the difference in a little detail and simple manner please

• Please add more details. Why do they look the same for you? Can you supply an example? Commented Nov 5, 2016 at 14:28
• I am learning statistics...Integration of f(x) and summation of f(x) are performed in the same way... By adding the values together... So i got confused and i realised until you don't have infitesimals in the equation they both look identical... Just give me a practical difference please.. It would be of great help Commented Nov 5, 2016 at 14:34

In most simple words-

Summation- Sum of a small numbers of large quantities.

Integration- Sum of a large numbers of small quantities.

Other Simple Difference can be-

The Summation is a discrete sum whereas Integration is a continuous sum.

Example:

Here dx is an infinitesimal so that the integral summation is continuous.

Hope it helps, cheers! :)

• Glad, I could help man. Update me if you need any other help. Cheers! Commented Nov 5, 2016 at 14:38
• Abhishek bhai what if rather than using 1^2+ 2^2 +3^2...... What if i use 1^2+ 1.001^2+1.002^2+1.003^2..... Till n square... Wouldn't that be same... I mean discrete word is quite arbitrary in reality i could use this and will come close to result.. isn't it Commented Nov 5, 2016 at 14:42
• Observe the 2nd difference closely. Actually, Integration can be interpreted as a special form of summation. In numerical computation methods, integration is always performed as a summation so we always need to be sure about it. Now coming to your query- Yes, you can but see as you said you'll be close to the result and that matters in the terms of accuracy. So It's better it use as per the computation and requirement. Commented Nov 5, 2016 at 14:50
• Please answer this query as well Commented Nov 5, 2016 at 14:50
• In practise summation is what we do while calculating integration of unknown equations but in theory or maths we take epsilon or dx an arbitory small number that approach to zero and derive an equation out of it. Am i interpreting it right Commented Nov 5, 2016 at 14:53