Question

A function $f\left(x\right)$ is given as

$x$	0	1	2	3	4
$f\left(x\right)$	0.5	0.25	0.1	0.05	0.029

The value of ${\int }_0^{4}f\left(x\right)dx$ as evaluated by Simpson's $\frac{1}{3}$ rule is ____

• A. 0.64

Answer 1

The correct option is A 0.64
${\int }_0^{4}f\left(x\right)dx=\frac{h}{3}[(y_0+y_4)+4(y_1+y_3)+2y_2]$

$=\frac{1}{3}[(0.5+0.029)+4(0.25+0.05)+2\times 0.1]\simeq 0.64$