Hello,
Reminders:
\($\sum_{i=1}^{n} i= \dfrac{n(n+1)}{2}$\)
\($ \sum_{i=1}^{n} i^2= \dfrac{n(n+1)}{2}$\)
\($ \sum_{i=1}^{n} i^3= \dfrac{n^2(n+1)^2}{4} $\)
\(n=6\\
x_{0}=0\\
x_{n}=3\\
\Delta= \dfrac{x_n-x_0}{n}=0.5\\\)
\(x_{i} =0+\Delta*i= \frac{i}{2}\)
\($ \sum_{i=1}^{n}\ \Delta*f(x_{i})=\sum_{i=1}^{6}\ \dfrac{i^3/8-6i}{2} $\)
\($= \dfrac{1}{2}\sum_{i=1}^{6} (\frac{i^3}{8} -6i)=\dfrac{1}{16}*\frac{(6*7)^2}{4}- \frac{9*7}{2}= -3.9575\)
