Is that any examples that can combine function, limit, differentiation and integration into one?
1 Answer
I'm not sure quite what you mean, but see below for my attempt at an answer (i.e. an example which incorporates limits, functions, derivatives, and integrals).
Explanation:
Here is my example:
Let
First comes the integration, in finding
Hence we are finding
It just so happens that if we differentiate
Using the chain rule
This gives a derivative of
Using the product rule to differentiate
Hence
Thus our integral becomes:
(Remember
Now to find
Doing a bit of rearrangement we get:
Easily enough we can simply let
Hence it just becomes:
I hope this helps.