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(sin^(-1)sqrtx-cos^(-1)sqrtx)/(sin^(-1)s...

`(sin^(-1)sqrtx-cos^(-1)sqrtx)/(sin^(-1)sqrt(x)+cos^(-1)sqrtx)`

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int (sin^-1sqrtx-cos^-1 sqrtx)/(sin^-1 sqrtx+ cos^-1 sqrtx)

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Knowledge Check

  • int(sin^(-1)sqrtx-cos^(-1)sqrtx)/(sin^(-1)sqrtx+cos^(-1)sqrtx)dx=

    A
    `2/pi[sqrt((x-x^2))+(1-2x)sin^(-1)sqrtx]+x`
    B
    `2/pi[sqrt((x-x^2))-(1-2x)sin^(-1)sqrtx]-x`
    C
    `2/pi[sqrt((x-x^2))+(1-2x)sin^(-1)sqrtx]-x`
    D
    None

  • f(x)=sqrtx-(1)/(sqrtx)

    A
    `I_(1)=(0, infty), I_(2)= phi`
    B
    `I_(1) = phi , I_(2)=(0, infty)`
    C
    `I_(1)= phi, I_(2)=(- infty, 0)`
    D
    none of these

  • If y=sec^(-1)""(sqrtx+1)/(sqrtx-1)+sin^(-1)""(sqrtx-1)/(sqrtx+1) , then (dy)/(dx) is equal to

    A
    0
    B
    `(1)/(sqrtx+1)`
    C
    1
    D
    3

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