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