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int0^(pi/2)(dx)/(1+2cosx)...

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

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int_(0)^(pi//2)(dx)/(2+cosx)=

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

Knowledge Check

  • int_(0)^(pi//2)(dx)/(2+cosx)=

    A
    `1/(sqrt(3))tan^(-1)(1/(sqrt(3)))`
    B
    `sqrt(3)tan^(-1)(sqrt(3))`
    C
    `2/(sqrt(3))tan^(-1)(1/(sqrt(3)))`
    D
    `2sqrt(3)tan^(-1)(sqrt(3))`

  • The value of I=int_(0)^(pi//2) (1)/(1+cosx)dx is

    A
    `(pi)/(4)`
    B
    `(pi)/(2)`
    C
    1
    D
    `pi`

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