Question

$f\left(x\right)=\frac{1}{1+x}$ for $0\le x\le 1$ and the interval [0,1] is divided into 2 equal subintervals. UsingTrapezoidal rule, ${\int }_0^1\frac{1}{1+x}dx=$

• A. $\frac{17}{24}$
• B. $\frac{17}{14}$
• C. $\frac{17}{48}$
• D. $\frac{17}{12}$

Answer 1

The correct option is A $\frac{17}{24}$

${\int }_a^{b}f\left(x\right)dx=\frac{b-a}{2N}\left(f\right(x_1)+2f(x_2)+2f(x_3)+....2f(x_N)+f(x_{N+1}\left)\right)$
Since $N=2$
So,
${\int }_0^1\frac{1}{1+x}dx=\frac{1}{2\times 2}\left[f\right(0)+2f(0.5)+f(1\left)\right]$
$=\frac{1}{4}[1+4/3+1/2]$
$=\frac{17}{24}squnits$