Question: Integral of product of vector function and its derivative

Hi all.

Assume that we have partitioned [0,a], into N equidistant subintervals and in each subinterval we have M sets of poly nomials of the following form:

where Tm(t)=tm( namely Taylor Series) and tf is a(final point)
for Example with N=4, M=3 we have:

now we want to approximate a function, asy f(t), in this interval with following form:

Assume that we have

where '"." means common derivetive. How can we do the later integran in right way?

Note that t is unknown

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

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