proof of the fundamental theorem of calculus
is well defined.
Consider the increment of :
since as . This proves the first part of the theorem.
For the second part suppose that is any antiderivative of , i.e. . Let be the integral function
We have just proven that . So for all or, which is the same, . This means that is constant on that is, there exists such that . Since we have and hence for all . Thus
|Title||proof of the fundamental theorem of calculus|
|Date of creation||2013-03-22 13:45:37|
|Last modified on||2013-03-22 13:45:37|
|Last modified by||paolini (1187)|