# Math Help - basic difference between summation and integration

1. ## basic difference between summation and integration

can you plz tell me what is the basic difference between summation and integration..? i was going through the Poisson distribution function and in one case it was discrete and we had to make summation to get the result and other cases for continuous function we integrated it...now what is meant by discrete and continuous in probability and why do we integrate or sum up in different cases?

2. ## Re: basic difference between summation and integration

Integration is a way to "sum over (usually uncountable) infinite sets", while sums just sum over finite sets. Series are sums over countable sets.
The integral is a more general, more powerful version of a sum. But if you can use a sum (because you can count the number of possible values), it is usually easier.

3. ## Re: basic difference between summation and integration

With summation, you're summing an expression for discrete values (such as 1,2,3...) while for integration, you're summing along the entire range of values.

For example, suppose you want to find the area under the curve $y = x^2$ from x = 0 to x = k. A common approach to approximate this is use rectangles of width 1 and use a summation:

$\sum_{i=0}^{k-1} i^2$

However, as the width of your rectangles decreases to an infinitely small length dx, your sum gets closer and closer to the desired area, which is given by the integral

$\int_{0}^{k} x^2 \, dx$

The integral sign functions exactly the same way as a sigma, but you are summing over a continuous range of numbers.

Integral - Wikipedia, the free encyclopedia