Question

Area bounded by the curve y = maxi {sinx, cosx} and x-axis , between the lines x = $\frac { \pi } { 4 }$and x = 2nis equal to

• A. $\frac { ( 4 \sqrt { 2 } - 1 ) } { \sqrt { 2 } }$sq. units
• B. $( 4 \sqrt { 2 } - 1 )$sq. units
• C. $\frac { ( 4 \sqrt { 2 } - 1 ) } { 2 }$sq. units
• D. None of these

Answer 1

Answer: (A)

$\frac { ( 4 \sqrt { 2 } - 1 ) } { \sqrt { 2 } }$sq. units

Answer 2

Bold lines represents the graph of y = maxi.{sinx, cosx}.

Required area,

$\Delta = \int _ { \pi / 4 } ^ { \pi } \sin x d x - \int _ { \pi } ^ { 5 \pi / 4 } \sin x d x$

$= - \left. \cos x \right| _ { \pi / 4 } ^ { \pi } + \left. \cos x \right| _ { \pi } ^ { 5 \pi / 4 } - \left. \sin x \right| _ { 5 \pi / 4 } ^ { 3 \pi / 2 } + \left. \sin x \right| _ { 3 \pi / 2 } ^ { 2 \pi }$

$= \frac { ( 4 \sqrt { 2 } - 1 ) } { \sqrt { 2 } }$ sq. units.