Lorena Beard

2022-07-01

Given the following data on $y=f\left(x\right)$,
$\overline{)\begin{array}{cc}\text{x}& \text{y}\\ 0& 32\\ 1& 38\\ 2& 29\\ 3& 33\\ 4& 42\\ 5& 44\\ 6& 38\end{array}}$
Calculate approximately ${\int }_{0}^{6}f\left(x\right)dx$.

Brendan Bush

Expert

Using Simpson's rule, ${\int }_{0}^{6}f\left(x\right)dx\approx 224.$
For comparison, using the trapezoidal rule, the answer would be ${\int }_{0}^{6}f\left(x\right)dx\approx \frac{1}{2}\left(6\right)\left(32+38\right)=210.$.

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