Question

Area of the region bounded by the curve $y = tan\,x$, line $x=\frac{\pi}{4}$ and the $x$-axis is

• A. log $2$ sq. units
• B. $\frac{1}{2} log \,2 $ sq. units
• C. $\frac{1}{3} log \,2 $ sq. units
• D. $5 \, log \, 2$ sq. units

Answer 1

Answer: (B)

We have, $y = tan\,x ...\left(i\right)$ between $x=\frac{\pi}{4}$ and $x$-axis.

Required area = area of shaded region
$=\int\limits_{0}^{\pi / 4 }tan \,x dx$
$=\left[-log\left|cos\,x\right|\right]_{0}^{\pi/ 4}=-log \frac{1}{\sqrt{2}}+log \,1$
$=log \sqrt{2}=\frac{1}{2}log\,2 $ sq. units