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The value of definite integrals int0^(2p...

The value of definite integrals `int_0^(2pi)(max(sinx ,cosx)-mindot(sinx ,cosx))dx` is equal to

Answer

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Given int_(0)^(pi//2)(dx)/(1+sinx+cosx)=A . Then the value of the definite integral int_(0)^(pi//2)(sinx)/(1+sinx+cosx)dx is equal to

Given int_(0)^(pi//2)(dx)/(1+sinx+cosx)=A . Then the value of the definite integral int_(0)^(pi//2)(sinx)/(1+sinx+cosx)dx is equal to

Knowledge Check

  • Given int_(0)^(pi//2)(dx)/(1+sinx+cosx)=A . Then the value of the definite integral int_(0)^(pi//2)(sinx)/(1+sinx+cosx)dx is equal to

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

  • The value of the integral int_(0)^((pi)/(2))|sinx-cosx|dx is -

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

  • The value of the definite integral int_(2pi)^(5pi//2)(sin^(-1)(cosx)+cos^(-1)(sinx))dx is equal to

    A
    `(pi^(2))/(8)`
    B
    `(pi^(2))/(4)`
    C
    `(pi^(2))/(2)`
    D
    `pi^(2)`

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