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Triss [41]
3 years ago
8

Evaluate the Riemann sum for (x) = x3 − 6x, for 0 ≤ x ≤ 3 with six subintervals, taking the sample points, xi, to be the right e

ndpoint of each interval. Give three decimal places in your answer.
Mathematics
2 answers:
DENIUS [597]3 years ago
8 0
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


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Marta_Voda [28]3 years ago
5 0

Answer:

incorrect its -3.9375

Step-by-step explanation:

https://www.coursehero.com/file/18659738/Module5/

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