Question

Using Simpson's rule, by taking 4 equal parts, the value of ${\int }_1^5\frac{1}{x}dx=?$

• A. $1.58$
• B. $1.62$
• C. $1.75$
• D. $2.3$

Answer 1

The correct option is B $1.62$

Let $f\left(x\right)=\frac{1}{x}$
$h=\frac{b-a}{n}$
$=\frac{5-1}{4}=1$
Interval has to be 1,for 4 equal parts.
Hence $f\left(1\right)=1$
$f\left(2\right)=0.5$
$f\left(3\right)=0.33$
$f\left(4\right)=0.25$
$f\left(5\right)=0.2$
Hence applying Simpson's rule rule we get
$△=\frac{h}{3}\left[f\right(1)+4(f_2+f_4)+2(f\left(3\right))+f_5]$
$=\frac{1}{2}[1+0.2+4[0.5+0.25]+2[0.334\left]\right]$
$=1.6\overline{2}$