If ${I_1} = \mathop \smallint \limits_{1 - k}^k \,\,x\,\,\sin \,\,\left\{ {x\left( {1 - x} \right)} \right\}\,\,dx$ and ${I_2} = \mathop \smallint \limits_{1 - k}^k \,\,\sin \,\,\left\{ {x\left( {1 - x} \right)} \right\}\,\,dx$, then

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

{I_1} = \int \limits_{1 - k}^k \,\,x\,\,\sin \,\,\left\{ {x\left( {1 - x} \right)} \right\}\,\,dx

and

{I_2} = \int \limits_{1 - k}^k \,\,\sin \,\,\left\{ {x\left( {1 - x} \right)} \right\}\,\,dx

, then

View answer and explanation

Correct option: B

2\,{I_1} = {I_2}

Option B (

2\,{I_1} = {I_2}

) is correct because by using the property of definite integrals and algebraic manipulation, we can derive this relationship.

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