# 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 and drumist

#### 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