Integrating a linear polynomial approx

Nov 2009
75
0
hi,

thanks for reading.can anyone help me out?(Crying)
see the attached file.i am working out for many hours how to integrate P1(t). does anyone know?
how do you get -1/2hf(..... ) + 3/2hf(....) ?
thats all i need to know!
i tried integrating MANY times. it looks easy.so what am i not understanding?

thanks all
 

Attachments

Nov 2008
1,458
646
France
Hi

The first integral is

\(\displaystyle \left[\frac{t^2}{2}-t_it\right]_{t_i}^{t_{i+1}} = \frac{t_{i+1}^2}{2}- t_i t_{i+1}+\frac{t_i^2}{2}\)

Substituting \(\displaystyle t_{i+1} = t_i + h\)

\(\displaystyle \left[\frac{t^2}{2}-t_it\right]_{t_i}^{t_{i+1}} = \frac{t_{i}^2}{2} + h t_i + \frac{h^2}{2} - t_i^2 - h t_i + \frac{t_i^2}{2} = \frac{h^2}{2}\)
 
Nov 2009
75
0
Hi

The first integral is

\(\displaystyle \left[\frac{t^2}{2}-t_it\right]_{t_i}^{t_{i+1}} = \frac{t_{i+1}^2}{2}- t_i t_{i+1}+\frac{t_i^2}{2}\)

Substituting \(\displaystyle t_{i+1} = t_i + h\)

\(\displaystyle \left[\frac{t^2}{2}-t_it\right]_{t_i}^{t_{i+1}} = \frac{t_{i}^2}{2} + h t_i + \frac{h^2}{2} - t_i^2 - h t_i + \frac{t_i^2}{2} = \frac{h^2}{2}\)


aha...! thats where confusion happened... h can be anything =S
a difference between one point and another. thanks! =D