Tiffanywongjm
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Evaluate the Riemann sum for (x) = x3 − 6x, for 0 ≤ x ≤ 3 with six subintervals, taking the sample points, xi, to be the right endpoint of each interval. Give three decimal places in your answer.

Respuesta :

caylus
Hello,

Reminders:
[tex]$\sum_{i=1}^{n} i= \dfrac{n(n+1)}{2}$ [/tex]
[tex]$ \sum_{i=1}^{n} i^2= \dfrac{n(n+1)}{2}$ [/tex]
[tex]$ \sum_{i=1}^{n} i^3= \dfrac{n^2(n+1)^2}{4} $ [/tex]

[tex]n=6\\ x_{0}=0\\ x_{n}=3\\ \Delta= \dfrac{x_n-x_0}{n}=0.5\\ [/tex]
[tex] x_{i} =0+\Delta*i= \frac{i}{2} [/tex]

[tex]$ \sum_{i=1}^{n}\ \Delta*f(x_{i})=\sum_{i=1}^{6}\ \dfrac{i^3/8-6i}{2} $[/tex]
[tex]$= \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[/tex]


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