Integrating using Simpson's Rule

67 Views Asked by At

Suppose there are functions

$$ g(x) = \frac{(2 \cdot \lfloor x\rfloor)}{(3\cdot x - \lfloor x \rfloor)} \tag{1}$$

and

$$ f(x) =\frac{\mid g(x)\mid}{ g(x)} \tag{2} $$

Now how do we do the definite integral of $f(x)$ with limits $-10$ to $0$ using Simpson's rule.

Simpson's Rule states that integral of $f(x)$ limited from $a$ to $b$ is approx equal to

$$ \frac{b-a}{6} \cdot \left[f(b) + 4 \cdot f\left(\frac{a+b}{2}\right) + f(a) \right] \tag{3}$$

Putting $ f(0)$ returns an indeterminant value in the form of $0/0$ which cannot be used to carry out further Calculations. Hence what are we supposed to do in such a scenario?