# Simpson Rule Question

#### Paymemoney

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
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:

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

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

Paymemoney