A function F : T [right arrow] X is called an antiderivative
of f : T [right arrow] X provided
ii) Every ld-continuous function f has a [nabla] antiderivative
So, if we want to calculate the area of f we make use of the primitive function f(or the antiderivative
It is known that piecewise rd-continuous functions possess an antiderivative
It is noteworthy to mention that every rd-continuous function f has an antiderivative
n)] (x), n [member of] Z exists for [absolute value of x] < 1 (when for n < 0 it denotes the nth antiderivative
Few of us know precisely what algorithms our CAS uses in determining antiderivatives
, or why the CAS may fail to provide an antiderivative
on a particular example; however, good facility in hand-computation together with a CAS enables users to handle more sophisticated examples whenever they arise.
nj] (x) provide evaluation of an antiderivative
of a continuous function on the interval [0,1].
A function F: T [right arrow] R is called an antiderivative
of f: T [right arrow] R provided [F.
a]f(t)dt consists precisely of values of the definite integral, and that this path turns out to be an antiderivative
of the original function