Question

Area bounded by the curves y = sin^-1x, y-axis and y = cos^-1x is equal to

• A. (2 + $\sqrt { 2 }$) sq. units
• B. (2 – $\sqrt { 2 }$) sq. units
• C. (1+ $\sqrt { 2 }$) sq. units
• D. ($\sqrt { 2 }$− 1) sq. units

Answer 1

Answer: (B)

(2 – $\sqrt { 2 }$) sq. units

Answer 2

Required area,

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

$= - \left. \cos y \right| _ { 0 } ^ { \pi / 4 } + \left. \sin y \right| _ { \pi / 4 } ^ { \pi / 2 }$

$= - \frac { 1 } { \sqrt { 2 } } + 1 + 1 - \frac { 1 } { \sqrt { 2 } } = ( 2 - \sqrt { 2 } )$ sq. units.