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I=int((pi)/(6))^((pi)/(3))(sqrt(cosx))/(...

`I=int_((pi)/(6))^((pi)/(3))(sqrt(cosx))/(sqrt(cosx)+sqrt(sinx))dx` .
(i) Use the formula `int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx` in I.
(ii) Add the above result with given value of I.
(iii) Evaluate I

Text Solution

Verified by Experts

The correct Answer is:
`I=int_((pi)/(6))^((pi)/(3))(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx))dx` . . . . (2)
(ii) `(pi)/(6)`
(iii) `:.I=(pi)/(12)`.
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