Question

Area bounded by y = tan^-1x, y = cot^-1x and y-axis is equal to

• A. sq. units
• B. ln 4 sq. units
• C. ln8 sq. units
• D. ln 2 sq. units

Answer 1

Answer: (D)

ln 2 sq. units

Answer 2

Required area,

$\Delta = \int _ { 0 } ^ { \pi / 4 } \tan y d y + \int _ { \pi / 4 } ^ { \pi / 2 } \cot y d y$

$= \ln \sqrt { 2 } - \ln \frac { 1 } { \sqrt { 2 } } = \ln 2$