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Len N be set of natural numbers. For n...

Len N be set of natural numbers. For `n in N` defiine
`I_(n)=int_(0)^(pi) (x sin^(2n)(x))/(sin^(2n)(x)+cos^(2n)(x)) dx`.
Then for `m,n in N`

A

`I_m lt I_n` for all `m lt n`

B

`I_m gt I_n ` for all `m lt n`

C

`I_m = I_n` for all `m ne n`

D

` I_m lt I_n ` for some ` m le n ` and `I_m gt I_n ` for some `m lt n`

Text Solution

Verified by Experts

The correct Answer is:
C
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