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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
If $I = \int\limits_0^{\frac{\pi }{2}} {\cos \left( {\sin x} \right)} \,dx,J = \int\limits_0^{\frac{\pi }{2}} {\sin \left( {\cos x} \right)} \,dx$ and $K = \int\limits_0^{\frac{\pi }{2}} {\cos x} \,dx$ , then
  • A
    $K>I>J$
  • B
    $J>I>K$
  • C
    $I>J>K$
  • ✓
    $I>K>J$
✓

Answer

Correct option: D.
$I>K>J$
d
$\cos (\sin x)>\cos x>\sin (\cos x)$ for $x \in\left(0, \frac{\pi}{2}\right)$

$\int_0^{\pi /2} {\cos } (\sin x)dx > \int_0^{x/2} {\cos } \,x\,dx > \int_0^{x/2} {\sin } (\cos x)dx \Rightarrow I > K > J$

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