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Prove that: int(0)^(pi//2) (sinx)/(sinx ...

Prove that: `int_(0)^(pi//2) (sinx)/(sinx +cos x) dx =(pi)/(4)`

A

`(pi)/(2)`

B

`pi`

C

`(pi)/(4)`

D

none

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • int_(0)^(pi//2) (sinx )/(sin x + cos x ) dx=

    A
    `pi/4`
    B
    `pi/2`
    C
    `(3pi)/4`
    D
    `(3pi)/2`

  • int_(0)^(pi//2) (sin x) / ((sinx + cosx)^(2) ) dx =

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

  • int_(0)^(pi//2)e^(x)sinx dx=

    A
    `1/2(e^((pi)/2)-1)`
    B
    `1/2(e^((pi)/2)+1)`
    C
    `1/2(1-e^((pi)/2))`
    D
    `2(e^((pi)/2)+1)`

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