${I_1} = \mathop \smallint \nolimits_0^{\pi /2} \,\,\sin \,\,x\,\,dx,\,\,{I_2} = \mathop \smallint \nolimits_0^{\pi /2} \,\,{\sin ^3}\,\,x\,\,dx$ then

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

{I_1} = \int \nolimits_0^{\pi /2} \,\,\sin \,\,x\,\,dx,\,\,{I_2} = \int \nolimits_0^{\pi /2} \,\,{\sin ^3}\,\,x\,\,dx

then

View answer and explanation

Correct option: A

{I_1}\,\,\, > \,\,\,{I_2}

Option A is correct because sin(x) is greater than sin³(x) in the interval [0, pi/2], therefore the integral of sin(x) is greater than the integral of sin³(x).

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