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int((pi)/(6))^((pi)/(3))(dx)/(1+sqrt(tan...

`int_((pi)/(6))^((pi)/(3))(dx)/(1+sqrt(tanx))=(pi)/(12)`

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Statement-I : The value of the integral int_((pi)/(6))^((pi)/(3))(dx)/(1+sqrt(tanx)) is equal to (pi)/(6) . Statement-II : int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx

The value of int_((pi)/(6))^((pi)/(3)) (dx)/(1+sqrt(tan x)) is equal to -

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int_(0)^((pi)/(4))(dx)/(1+sinx)

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The value of int_((pi)/(4))^((3pi)/(4))(dx)/(1+cosx) is -

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int_((pi)/4)^((pi)/2)(2cosecx)^17 dx

Prove that, int_((pi)/(4))^((3pi)/(4))(phidphi)/(1+sinphi)=(sqrt(2)-1)pi

int_(2)^(3)(dx)/(sqrt(6x-x^(2)-5))=(pi)/(6)