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int(0)^(pi/2)(cos^(5)x dx)/(sin^(5)x+cos...

`int_(0)^(pi/2)(cos^(5)x dx)/(sin^(5)x+cos^(5)x)`

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To solve the integral \[ I = \int_{0}^{\frac{\pi}{2}} \frac{\cos^5 x}{\sin^5 x + \cos^5 x} \, dx, \] we can use a property of definite integrals. Specifically, we can use the substitution \( x = \frac{\pi}{2} - t \). ...
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Explore conceptually related problems

(i) int_(0)^(pi//2)(sin^(7)x)/((sin^(7)x+cos^(7)x))dx=(pi)/(4) (ii) int_(0)^(pi//2)(sin^(5)xdx)/((sin^(5)x+cos^(5)x))dx=(pi)/(4)

Prove that : int_(0)^(pi//2) (cos^(5))/(sin^(5) x+cos^(5) x)dx= (pi)/(4)

Knowledge Check

  • int_(0)^(pi//2) (cos^(5)x)/(sin^(5)x+cos^(5)x)dx is equal to

    A
    0
    B
    `pi/3`
    C
    `pi/4`
    D
    `pi/2`

  • int_(0)^(pi//2) (dx)/(4sin^(2) x + 5 cos^(2)x)

    A
    `(pi)/(2sqrt(5))`
    B
    `pi/4`
    C
    `(pi)/(4sqrt(5))`
    D
    `(pi)/sqrt(5)`

    • Similar Questions

    Explore conceptually related problems

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

    I=int_(0)^(2 pi)cos^(5)x*dx

    int_(0)^(pi/2)sin^(6)x cos^(5)xdx=

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