If $I = \mathop \smallint \nolimits_0^{\pi /2} \,\,{\rm{cos}}\,\,(\sin \,\,x)\,\;dx$, $J = \mathop \smallint \nolimits_0^{\pi /2} \,\,\sin \,\,(\cos \,\,x)\;dx\;\,\,{\rm{and\;}}\,\,K = \mathop \smallint \nolimits_0^{\pi /2} \cos \,\,x\,dx.\,{\rm{Then}},$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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I = \int \nolimits_0^{\pi /2} \,\,\mathrm{cos}\,\,(\sin \,\,x)\,\;dx

J = \int \nolimits_0^{\pi /2} \,\,\sin \,\,(\cos \,\,x)\;dx\;\,\,\mathrm{and\;}\,\,K = \int \nolimits_0^{\pi /2} \cos \,\,x\,dx.\,\mathrm{Then},

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Correct option: D

I > K > J

Option D (

I > K > J

) is correct because, within the interval [0, π/2], cos(sin x) > cos x > sin(cos x), leading to the given inequality of integrals.

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