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underset(0)overset(pi//2)(sin^(5)x)/(sin...

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

Text Solution

Verified by Experts

The correct Answer is:
`I-pi/4`
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Find int_(0)^(pi//2) (sin^(5)x)/(sin^(5)x + cos^(5)x)dx

underset(0)overset(pi//2)(dx)/(4+5cosx)

Knowledge Check

  • int sin^(5) x. cos^(5) x dx =

    A
    `(cos^(6)x)/(60) (6 sin^(4) x + 3 sin^(2) x + 1) + c`
    B
    `- (sin^(6) x)/(60) (6 cos x + 3 cos^(2) x + 1) + c `
    C
    `-(cos^(6)x)/(60) (6 sin^(4) x + 3 sin^(2) x + 1) + c `
    D
    `(sin^(6) x)/(60) (6cos^(4) x + 3cos^(2) x + 1) + c `

  • int_(0)^(pi//2) (16sin x. cos x)/(sin^(4) x + cos^(4)x)dx=

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

    • Similar Questions

    Explore conceptually related problems

    Evaluate the integrals . int_(0)^(pi//2) (sin^(5)x)/(sin^(5)x + cos^(5)x)dx

    By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(cos^(5)xdx)/(sin^(5)x+cos^(5)x)

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

    Evaluate int_(0)^(pi//2) (cos^(5//2)x)/(sin^(5//2)x=cos^(5//2)x)dx

    Evaluate the following integrals (i) int_(0)^(pi/2)(cos^(5//2)x)/(sin^(5//2)x+cos^(5//2)x)dx

    Evaluate the integrals . int_(0)^(pi//2) (sin^(2)x-cos^(2)x)/(sin^(3)x+cos^(3)x)dx

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