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Question
`int_0^(pi/2) 1/(1 + cosx) "d"x` = ______.
Options
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MCQ
Fill in the Blanks
Solution
`int_0^(pi/2) 1/(1 + cosx) "d"x` = 1.
Explanation:
`int_0^(pi/2) 1/(1 + cosx) "d"x = int_0^(p/2) 1/(2cos^2(x/2)) "d"x`
= `1/2 int_0^(pi/2) sec^2(x/2)"d"x`
= `1/2[(tan(x/2))/(1/2)]_0^(pi/2)`
= `tan pi/4 - tan 0`
= 1
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