Answer
$$-14.666$$
Work Step by Step
Given$$\int_{3}^{5} (9-x^2) d x, \quad N=4 $$
Since $\Delta x=\dfrac{b-a}{N}=0.5$ , then by using Simpson’s rule
\begin{align*}
S_{n}&=\dfrac{\Delta x}{3}\left[f(x_0)+4f(x_1)+2f(x_2)+4f(x_3).....+4f(x_{n-1})+f(x_n)\right]\\
S_{4}&=\dfrac{\Delta x}{3}\left[f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+ f(x_{4}) \right] \\
&=\dfrac{1}{6}\left[f(3)+4f(3.5)+2f(4)+4f(4.5)+ f(5) \right]\\
&\approx -14.666
\end{align*}
