Question

What is the area bounded by $y=\tan x$, $y=0$ and $x=\frac{\pi }{4}$?

• A. $\ln \sqrt{2}$ square units
• B. $\frac{\ln 2}{3}$ square units
• C. $2\left(\ln 2\right)$ square units
• D. None of the above

Answer 1

The correct option is A $\ln \sqrt{2}$ square units

The required area is,

${\int }_0^{\frac{\pi }{4}}\tan xdx$

$={[-\ln \cos x]}_0^{\frac{\pi }{4}}$

$=-\ln \left(\frac{1}{\sqrt{2}}\right)+\ln \left(1\right)$

$=\ln \sqrt{2}$