$$ \text { The values of a function } f \text { obtained for different values of } x \text { are shown in the table below. } $$

$$ \begin{array}{|c|c|c|c|c|c|} \hline x & 0 & 0.25 & 0.5 & 0.75 & 1.0 \\ \hline f(x) & 0.9 & 2.0 & 1.5 & 1.8 & 0.4 \\ \hline \end{array} $$

$$ \text { Using Simpson's one-third rule, } $$

$$ \int_0^1 f(x) d x \approx $$__________[Rounded off to 2 decimal places]

In the closed interval $[0,3]$, the minimum value of the function $f$ given below is $f(x)=2 x^3-9 x^2+12 x$

If $C$ is the unit circle in the complex plane with its center at the origin, then the value of $n$ in the equation given below is _______ (rounded off to 1 decimal place).

$$ \oint_c \frac{z^3}{\left(z^2+4\right)\left(z^2-4\right)} d z=2 \pi i n $$

The directional derivative of the function $f$ given below at the point $(1,0)$ in the direction of $\frac{1}{2}(\hat{i}+\sqrt{3} \hat{j})$ is _______ (Rounded off to 1 decimal place).

$$ f(x, y)=x^2+x y^2 $$