Question

Evaluate :`int_0^(pi/2)1/(1+cosx)dx`

 

Answer 1

`int_0^(pi/2)1/(1+cosx)dx`

Solving the integral without limits,

`int1/(1+cosx)dx`

`=int1/(2cos^2 (x/2))dx`

`=1/2intsec^2 (x/2)dx`

`=1/2[tan(x/2)/(1/2)]+C`

`=tan(x/2)+C`

Substituting the limits,we get

`=[tan(x/2)]_0^(pi/2)`

`=[tan (pi/4)-tan0]`

 = 1