Question

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

• A. log $2$ sq. units
• B. $\frac{1}{2}log2$ sq. units
• C. $\frac{1}{3}log2$ sq. units
• D. $5log2$ sq. units

Answer 1

Answer: (B)

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

Required area = area of shaded region
$=\underset{0}{\overset{\pi /4}{\int }}tanxdx$
$={\left[-log\left|cosx\right|\right]}_0^{\pi /4}=-log\frac{1}{\sqrt{2}}+log1$
$=log\sqrt{2}=\frac{1}{2}log2$ sq. units