Question

The area occupied between the curve $xy=a^2,$ the vertical lines $x=a,x=4a(a>0)$ is

• A. $a^2\ln 2$
• B. $2a^2\ln 2$
• C. $a\ln 2$
• D. $2a\ln 2$

Answer 1

The correct option is B $2a^2\ln 2$


Given $xy=a^2$
$\Rightarrow y=\frac{a^2}{x}$
$A=\underset{a}{\overset{4a}{\int }}\frac{a^2}{x}dx$
$=a^2{\left[\ln |x|\right]}_a^{4a}$
$=a^2\ln 4=2a^2\ln 2$