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Prove that: int0^(pi//2)(sin x)/(sinx...

Prove that: `int_0^(pi//2)(sin x)/(sinx-cosx)dx=pi/4`

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int_(0)^(pi//2)(x)/(sinx+cosx)dx .

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

Knowledge Check

  • int_0^(pi//4)((x)/(xsinx+cosx)^2)dx

    A
    `(4-pi)/(4+pi)`
    B
    `(4+pi)/(4-pi)`
    C
    `(4-pi)/(3+pi)`
    D
    `(3+pi)/(4-pi)`

  • 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) abs(sinx-cosx) dx=

    A
    0
    B
    `sqrt(2) -1`
    C
    `2sqrt(2)-2`
    D
    `2sqrt(2) +2`

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    Evaluate: int_0^(pi//2)x/(sinx+cosx)dx

    int_(0)^(pi//2) e^x(sinx+cosx) dx

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