Second Fundamental Theorem


To understand what this Theorem is saying, do the following:

Is your derivative equal to f(x)?

The Second Fundamental Theorem says that when any function f(t) is integrated from 0 to x to get F(x), the derivative of this function F(x) is f(x).

 

Whatever f(t) is we can define F(x) to be the integral from 0 to x of f(t).

So if f(t) = Si ( ln ( J(t) ), where J(t) is some mysterious Bessel function, we can define F(x) to be the integral from 0 to x of this function.

 

You should pick several functions for f(t)--functions you can integrate--and integrate each from 0 to x. 

You should also graph your original function and construct the graph of the integral from 0 to x.