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Question: Finding the integral of a piecewise function

Question:Finding the integral of a piecewise function

student_1 305 Maple 2020
integration piecewise
January 16 2021
2

The interval [0,T] is divided into n subintervals [i*h, (i + 1)*h], i = 0,1,2, . . . ,n -1, of equal lengths h where h=T/n.

The first (n + 1) hat functions   is defined as follows:

 

Question:

How to find g_ij ( the value of the following integral)

=

where 

i = 0,1,2, . . . ,n -1,

alpha>0,

0<=t<h.

 

In fact, 

by using the Maple, I want to check whether it is equal to the following expression or not:
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