Question

Area between y = |cos^–1(sin x)| – |sin^–1(cos x)| and x-axis, where x Î $\left[ \frac { 3 \pi } { 2 } , 2 \pi \right]$ is -

• A. $\frac { \pi } { 2 }$
• B. $\frac { \pi ^ { 2 } } { 2 }$
• C. $\frac { \pi ^ { 2 } } { 4 }$
• D. $\frac { \pi } { 4 }$

Answer 1

Answer: (C)

$\frac { \pi ^ { 2 } } { 4 }$

Answer 2

r = |cos^–1 (sinx)| – |sin^–1(cosx)|

= |cos^–1 cos| – |sin^–1 sin $\left( \frac { \pi } { 2 } + x \right)$ | = $\left| \frac { 5 \pi } { 2 } - x \right|$ – = 4p –2x \ desired area = = $\frac { \pi ^ { 2 } } { 4 }$