Q. If $I = \int_{0}^{\pi/2}{cos(\sin{x)\ dx,}}$ $J = \int_{0}^{\pi/2}{\sin{(\cos{x)\ dx\ and\ K = \int_{0}^{\pi/2}{\cos{x\ dx.Then,}}}}}$
A) $K > I > J$
B) $J > I > K$
C) $I > J > K$
D) $I > K > J$
Explanation
(d)
Since, $cos(sin\ x) > \cos{x > \sin{(\cos{x),\ for\ x\ \in \left\lbrack 0,\frac{\pi}{2} \right\rbrack}}}$
$\Rightarrow \int_{0}^{\pi/2}{cos(\sin{x)dx > \int_{0}^{\pi/2}{\cos{x\ dx}}}}$
$> \int_{0}^{\pi/2}{\sin{(\cos{x)dx}}}$
$\Rightarrow \ I > K > J$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.