Question

The area bounded by the curve $y=\frac{1}{x^2}$ and its asymptote between the lines $x=1$ to $x=3$ is

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{1}{2}$
• D. $\frac{1}{6}$

Answer 1

The correct option is B $\frac{2}{3}$


Given $y=\frac{1}{x^2}$
Asymptote is $x-$axis
$\therefore Area=\underset{1}{\overset{3}{\int }}\left(\frac{1}{x^2}\right)dx={[-\frac{1}{x}]}_1^3=-\frac{1}{3}-(-1)=\frac{2}{3}$