Question

Let $f\left(0\right)=1,f\left(0.5\right)=\frac{5}{4},f\left(1\right)=2,f\left(1.5\right)=\frac{3}{4}$ and $f\left(2\right)=5$.

Using Simpson's rule, ${\int }_0^{2}f\left(x\right)dx=?$

• A. $3$
• B. $\frac{7}{6}$
• C. $\frac{14}{9}$
• D. $\frac{7}{9}$

Answer 1

The correct option is A $3$

The required ans will be
$=\left(\frac{0.5}{3}\right)\left(f\right(0)+4(f\left(0.5\right)+f\left(1.5\right))+2(f\left(1\right))+f(2\left)\right]$
$=\frac{1}{6}(1+4(\frac{5}{4}+\frac{3}{4})+2(2)+5]$
$=\frac{1}{6}[1+8+9]$
$=\frac{1}{6}\left(18\right)$
$=3$