Question

Area of the region bounded by the curve $y = \tan x$ tangent drawn to the curve at $x = \frac { \pi } { 4 }$ and the x-axis is

• A. $\frac { 1 } { 4 }$
• B. $\log \sqrt { 2 } + \frac { 1 } { 4 }$
• C. $\log \sqrt { 2 } - \frac { 1 } { 4 }$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Shaded area $= \int _ { 0 } ^ { \pi / 2 } \tan x d x$ $= [ \log \sec x ] _ { 0 } ^ { \pi / 4 }$

$= \log \sqrt { 2 } - \log 1$ $= \log \sqrt { 2 }$.