Question

lf [2,6] is divided into 4 intervals of equal length then approximate value of ${\int }_2^6\frac{1}{x^2-x}dx$ using Simpson's rule

• A. $0.3222$
• B. $0.2333$
• C. $0.5222$
• D. $0.2555$

Answer 1

Answer: (C)

$0.5222$

$h=\frac{b-a}{n}$
Here $b=6$ $a=2$ and $n=4$.
Hence $h=1$.
$f\left(2\right)=\frac{1}{2}=y_0$
$f\left(3\right)=\frac{1}{6}=y_1$
$f\left(4\right)=\frac{1}{12}=y_2$
$f\left(5\right)=\frac{1}{20}=y_3$
$f\left(6\right)=\frac{1}{30}=y_4$
Applying Simpson's rule, we get
$△=\frac{h}{3}[y_0+2(y_2)+4(y_1+y_3)+y_4]$
$=\frac{1}{3}[0.5+2(\frac{1}{12})+4(\frac{1}{6}+\frac{1}{20})+\frac{1}{30}]$
$=0.5\overline{2}$