# is there a difference between sum and integral?

is there a difference between integrating a function between two limits and summing a function and if so where does the difference come from and when would you use each method in real life situations

• What do you mean by "summing a function"? – fosho Jan 16 '16 at 16:44
• the sigma notation – AlexanderRD Jan 16 '16 at 16:45
• – user174622 Jan 16 '16 at 16:47
• do you have any background in measure theory? If yes, have a look at $\ell^p$ and $L^p$ spaces. And for an application it's very interesting to have a look at the expectation value of discrete and continuous random variables. – noctusraid Jan 16 '16 at 16:53
• well "summing a function" means to actually sum the values of the function at each point. integrating is summing the infinitesimal areas at each x between the limits. – Airdish Jan 16 '16 at 16:58