Question

The values of $f\left(x\right)$ for $x=0$,1,2,3,4,5,6 are given by 2,4, 10, 16,20,24,38 respectively then ${\int }_0^{6}f\left(x\right)dx$ by Using Simpson's rule is

• A. 90
• B. 91
• C. 92
• D. 93

Answer 1

Answer: (C)

92

Here $h=1$.
$f\left(0\right)=2=y_0$
$f\left(1\right)=4=y_1$
$f\left(2\right)=10=y_2$
$f\left(3\right)=16=y_3$
$f\left(4\right)=20=y_4$
$f\left(5\right)=24=y_5$
$f\left(6\right)=38=y_6$.
Using Simpson's rule, we get
$△=\frac{h}{3}[y_0+2[y_2+y_4]+4[y_1+y_3+y_5]+y_6]$
$=\frac{1}{3}[2+2[10+20]+4[4+16+24]+38]$
$=92$.