If ${I_1} = \mathop \smallint \nolimits_0^{\pi /2} \,\,x\,\,\sin \,\,x\,dx$ and ${I_2} = \mathop \smallint \nolimits_0^{\pi /2} \,x\,\,\cos \,\,x\,dx$, then which one of the following is true?

${I_2} - {I_1} = \frac{\pi }{2}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

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

and

{I_2} = \int \nolimits_0^{\pi /2} \,x\,\,\cos \,\,x\,dx

, then which one of the following is true?

View answer and explanation

Correct option: A

{I_1} + {I_2} = \frac{\pi }{2}

Option A (

{I_1} + {I_2} = \frac{\pi }{2}

) is correct because evaluating both integrals and summing them results in

\frac{\pi}{2}

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