int_(a)^(b)6dx

Prove that int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx and hence evaluate int_((pi)/(6))^((pi)/(3))(1)/(1+sqrt(tanx))dx.

Statement I int_((pi)/(6))^((pi)/(3))(1)/(1+tan^(3)x) is (pi)/(12) statement II int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx

what is int_(a)^(b)[x]dx+int_(a)^(b)[-x]dx equal to

int_(a)^(b)f(x)dx=int_(b)^(a)f(x)dx .

If int_(a)^(b)f(x)dx=int_(a)^(b)phi(x)dx , then-

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

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

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

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