`I_(1) = int_(pi/6)^(pi/3) (dx)/(1+sqrt(tanx))` and `I_(2) = (sqrt(sinx)dx)/(sqrt(sinx) + sqrt(cosx))`
What is `I_(1)` equal to ?

Options

A. `pi//24`
B. `pi//18`
C. `pi//12`
D. `pi//6`

Answer

C

Explanation

Adding `I_(1)` and `I_(3)`
`I_(1) +I_(2) = int_(pi/6)^(pi/3)(sqrt(sinx) + sqrt(cosx))/(sqrt(sinx) + sqrt(cosx)) dx int_(pi/6)^(pi/3) dx`
`= [x]_(pi/6)^(pi/3) = pi/6 = pi/12" "( :' I_(1) + I_(2) =2.)`