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For x epsilonR, and a continuous functio...

For `x epsilonR`, and a continuous function `f` let `I_(1)=int_(sin^(2)t)^(1+cos^(2)t)xf{x(2-x)}dx` and `I_(2)=int_(sin^(2)t)^(1+cos^(2)t)f{x(2-x)}dx`.
Then `(I_(1))/(I_(2))` is

A

`-1`

B

`1`

C

`2`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
B
`I_(1)=int_(sin^(2)t)^(1+cos^(2)t)xf(x(2-x))dx`
`=int_(sin^(2)t)^(1+cos^(2)t)(2-x)f(x(2-x))dx=2I_(2)-I_(1)`
or `2I_(1)=2I_(2)` or `(I_(1))/(I_(2))=1`
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