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The valued of int(sqrt(In2))^(sqrt(In3))...

The valued of `int_(sqrt(In2))^(sqrt(In3)) (x sinx^(2))/(sinx^(2)+sin(In 6-x^(2)))dx` is

A

`1/4 In 3/2`

B

`1/2 In 3/2`

C

`In 3/2`

D

`1/6 In 3/2`

Text Solution

Verified by Experts

The correct Answer is:
A
Put `x^(2)=t` and `2xdx=dt`
`:. I=1/2int_(In2)^(In3)(sint)/(sint+sin(In6-t)dt`
`=1/2int_(In2)^(In3)(sin(In6-t))/(sin(In6-t)+sint)dt`
`:.2I=1/2int_(In2)^(In3)1dt` or `I=1/4 In 3/2`
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