Simpson Rule Question

Dec 2008
509
2
Hi

Can someone tell me if this is correct:

Use Simpson's Rule with 10 subintervals to evaluate:
\(\displaystyle \int_{0}^{1} \frac{x}{x+2}\)

This is what i have done:

\(\displaystyle \int_{0}^{1} \frac{x}{x+2} = \frac{1}{30}[\frac{4}{21} + \frac{2}{11} +\frac{3}{23}+\frac{1}{6}+\frac{1}{5}+\frac{6}{13}+\frac{28}{27}+\frac{4}{7}+\frac{36}{29}+\frac{2}{3}]\)

\(\displaystyle \int_{0}^{1} \frac{x}{x+2} = 6.0054\)
 

skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
Hi

Can someone tell me if this is correct:

Use Simpson's Rule with 10 subintervals to evaluate:
\(\displaystyle \int_{0}^{1} \frac{x}{x+2}\)

This is what i have done:

\(\displaystyle \int_{0}^{1} \frac{x}{x+2} = \frac{1}{30}[\frac{4}{21} + \frac{2}{11} +\frac{3}{23}+\frac{1}{6}+\frac{1}{5}+\frac{6}{13}+\frac{28}{27}+\frac{4}{7}+\frac{36}{29}+\frac{2}{3}]\)

\(\displaystyle \int_{0}^{1} \frac{x}{x+2} = 6.0054\)
\(\displaystyle
\int_0^1 \frac{x}{x+2} \, dx \approx \frac{1}{30}\left(0 + \frac{4}{21} + \frac{2}{11} + \frac{12}{23} + \frac{1}{3} + \frac{4}{5} + \frac{6}{13} + \frac{28}{27} + \frac{4}{7} + \frac{36}{29} + \frac{1}{3}\right) = \) \(\displaystyle 0.189069...\)
 
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