Evaluate int((pi)/(6))^((pi)/(3))(sqrt(s...

Evaluate `int_((pi)/(6))^((pi)/(3))(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx))dx`

Answer

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By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx))dx

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

Knowledge Check

int_(0)^((pi)/(2))(f(sinx))/(f(cosx)+f(sinx))dx is :

A

`pi`

B

`(pi)/(2)`

C

`(pi)/(4)`

D

`(pi)/(8)`.

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