antiderivative

They should be familiar with the term "definite integral" and know how to find the antiderivative of a function.

It comes into our mind to seek for the integration of such functions f(x) power its antiderivative g(x).

(1) If F is any antiderivative of f on I, then (f" [e.sup.F])' = -[beta]f (f' - 1) [e.sup.F].

This antiderivative represents sort of average between the function u and its integral of order one.

The delta derivative of [xi] : T [right arrow] R is denoted by [[xi].sup.[DELTA]](t) and the operators antiderivative is denoted by [integral] [xi] (t)[DELTA]t.

The relationship between Prandtl stress functions corresponding to Lametensor fields [[LAMBDA].sub.n-1] and [[LAMBDA].sub.n] = ([h.sub.n-1] [omicron] [[PSI].sub.n-1]) [[LAMBDA].sub.n-1] is expressed by the formula [[PSI].sub.n] = [H.sub.n-1] [omicron] [[PSI].sub.n-1], with [H.sub.n-1] antiderivative of [h.sub.n-1] such that [[PSI].sub.n] is identically zero on the cross-sectional exterior boundary [partial derivative][[OMEGA].sub.0].

In [5-7], the antiderivative technique plays an essential role in proving their main results.

where [LAMBDA]'(-i[[partial derivative].sub.x]) = a[[partial derivative].sup.-2.sub.x] - b[[partial derivative].sup.2.sub.x], and the antiderivative [[partial derivative].sup.-1.sub.x] is defined by the Fourier transform such that

where C [member of] X is an arbitrary element independent of t and F is a pre- antiderivative of f.