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The Integral int(pi/4)^((3pi)/4)(dx)/(1+...

The Integral `int_(pi/4)^((3pi)/4)(dx)/(1+cosx)` is equal to: (2) (3) (4)

A

`-1`

B

`-2`

C

`2`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int_((pi)/4)^((3pi)/4)(dx)/(1+cosx)`………………i
`impliesI=int_((pi)/4)^((3pi)/4)(dx)/(1-cosx)`…………..ii
Adding i and ii we get
`2I=int_((pi)/4)^((3pi)/4)2/(sin^(2)x)dx`
`impliesI=int_((pi)/4)^((3pi)/4)cosec^(2)dx`
`impliesI=-(cotx)_(pi//4)^(3pi/4)=2`
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