Integrating a linear polynomial approx

matlabnoob

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

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running-gag

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 $$\displaystyle t_{i+1} = t_i + h$$

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

matlabnoob

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