# What is integration?

##### 1 Answer

Roughly speaking, integration is the inverse of differentiation, but there are several ways to think about it...

#### Explanation:

Given a suitably well behaved function

At any particular point

Integration covers a lot more cases than just Real valued functions of Real numbers. You can integrate over any kind of measurable set - e.g. a plane, a curve, a surface, a volume. The function that you are integrating may have any kind of value that is possible to sum and multiply by a scalar, e.g. Real, Complex, vector.

In such contexts you can think of an integral as a sort of infinite sum of values of a function over infinitesimally small pieces of the set over which you are integrating.

For example, suppose you have a function

#(int_(p in S) f(p) dp) / A#

If we split the surface of the sphere into a large number of little patches

#int_(p in S) f(p) dp ~~ sum_i A_i f(p_i)#