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int(0)^( pi/2)ln(sin^(2)x cos x)dx...

`int_(0)^( pi/2)ln(sin^(2)x cos x)dx`

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int_(0)^( pi/2)sin^(2)x cos x dx

int_(0)^(pi/2)(sin^(2)x*cos x)dx=

Knowledge Check

  • int_(0)^(pi)log sin^(2)x dx=

    A
    `2pilog_(e)(1/2)`
    B
    `pi log_(e)2`
    C
    `(pi)/2log_(e)(1/2)`
    D
    `pilog_(e)(1/2)`

  • If int_(0)^(pi//2)sin^(4)x cos^(2)x dx=(pi)/(32) , then int_(0)^(pi//2)sin^(2)x cos^(4)x dx=

    A
    `(pi)/(4)`
    B
    `(pi)/(8)`
    C
    `(pi)/(16)`
    D
    `(pi)/(32)`

  • Given that int_(0)^(pi//2) sin^(4) x cos^(2) x dx= (pi)/(32) , then int_(0)^(pi//2) cos^(4) x sin^(2) x dx =

    A
    `(pi)/(32)`
    B
    `(3pi)/(32)`
    C
    `(pi)/(2)`
    D
    none

    • Similar Questions

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    Prove that: int_(0)^( pi/2)log(sin^(3)x cos^(4)x)backslash dx=-(7 pi)/(2)log2

    int_(0)^(pi)log sin^(2)x dx=

    int_(0)^((pi)/(2))(x sin x*cos x)dx

    int_(0)^(pi//2) f(sin 2x) sin x dx= int_(0)^(pi//2) f(sin 2x) cos x dx= sqrt""2 int_(0)^(pi//4) f(cos 2x) cos x dx

    int_(0)^(pi//2) x sin x cos x dx

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