Question

The modulus of difference in values of ${\int }_0^1\frac{1}{1+x}dx$, evaluated using trapezoidal rule and Simpson's rule, taking h = 0.5. (correct upto 3 decimal places) is ________.

• A. 0.014

Answer 1

The correct option is A 0.014

x	0	0.5	1
$y=\frac{1}{1+x}$	1.000	0.6667	0.5

Trapezoidal rule gives,

$I=\frac{1}{4}[1.000+2(0.6667)+0.5]=0.7084$
Simpson's rule gives,

$I=\frac{1}{6}[1.000+4(0.6667)+0.5]=0.6945$

$\therefore |Difference|=|0.7084-0.6945|$
$=0.014$