fundamental theorem of integral calculus
Proof. We make the antithesis that there were on the interval two distinct points and with . Then the mean-value theorem guarantees a point between and such that
which value is distinct from zero. This is, however, impossible by the assumption of the theorem. So the antithesis is wrong and the theorem .
The contents of the theorem may be expressed also such that if two functions have the same derivative on a whole interval, then the difference of the functions is constant on this interval. Accordingly, if is an antiderivative of a function , then any other antiderivative of has the form , where is a constant.
|Title||fundamental theorem of integral calculus|
|Date of creation||2013-03-22 18:50:49|
|Last modified on||2013-03-22 18:50:49|
|Last modified by||pahio (2872)|