If ${u_{10}} = \mathop \smallint \limits_0^{\pi /2} \,\,{x^{10}}\,\,\sin \,\,x\;\,\,dx$, then the value of ${u_{10}}\,\, + \,\,90\;\,{u_8}$, is

$9\,\,{\left( {\frac{\pi }{2}} \right)^8}$

$9\,\,{\left( {\frac{\pi }{2}} \right)^9}\,$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

{u_{10}} = \int \limits_0^{\pi /2} \,\,{x^{10}}\,\,\sin \,\,x\;\,\,dx

, then the value of

{u_{10}}\,\, + \,\,90\;\,{u_8}

, is

View answer and explanation

Correct option: C

10\,\,{\left( {\frac{\pi }{2}} \right)^9}

Option C (

10\\,\,\left( {\frac{\pi }{2}} \right)^9

) is correct because by applying integration by parts twice, a recursive relationship between u_10 and u_8 is established, leading to the given result.

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