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The value of frac{120}{pi^3} |int0^pi fr...

The value of `frac{120}{pi^3}` `|int_0^pi frac{x^2 sin x cos x}{sin^4 x + cos^4 x} dx|` is

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int_0^pi sin^4x cos^4x dx

Evaluate: int_0^(pi//2)(xsinx cos\ x)/(sin^4x+cos^4x)dx

Knowledge Check

  • int_(0)^(pi//2) (x sin x cos x)/(sin^(4) x + cos^(4)x) dx =

    A
    `(pi^(2))/(8)`
    B
    `(pi^(2))/(16)`
    C
    `(pi^(2))/(32)`
    D
    `(pi^(2))/(4)`

  • int_0^(2pi) (x sin x cos x)/(cos^4 x+ sin^4 x) dx is equal to

    A
    `(pi^2)/4`
    B
    `(pi^2)/8`
    C
    `(pi^2)/16`
    D
    `(pi^2)/32`

  • int_(0)^(pi)sin 5 x cos 4x dx=

    A
    `(5)/(9)`
    B
    `(9)/(5)`
    C
    `(10)/(9)`
    D
    `(10)/(3)`

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    int_(0)^( pi/4)(sin x-cos x)dx

    int_(0)^(pi//4)(sin 2 x)/(sin^(4) x + cos^(4) x ) dx =

    int_(0)^(pi) dx/(3+2sin x + cos x) =

    The value of the integral int_0^(pi/4) frac{xdx}{sin^4 2x+cos^4 2x} equals:

    The value of int_0^(pi//2) (sinx-cos x)/(1+sin x cos x ) dx is

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