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Prove that: int0^(pi/4)(sqrt(tanx)+sqrt(...

Prove that: `int_0^(pi/4)(sqrt(tanx)+sqrt(cotx)\ dx=sqrt(2)dotpi/2`

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int_(0)^(pi//2)(sqrt(tanx)+sqrt(cotx))\ dx

Prove that : int_(0)^(pi//2) (sqrt(tanx))/(sqrt(tanx +sqrt(cotx)))dx=(pi)/(4)

Knowledge Check

  • int_(0)^(pi//4)(sqrt(tanx)+sqrt(cotx))dx equals

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

  • int_0^(pi//4)[sqrt(tanx)+sqrt(cotx)]dx is equal to

    A
    `sqrt2pi`
    B
    `pi/2`
    C
    `pi/sqrt2`
    D
    `2pi`

  • int_0^(pi//4) [sqrt((tan x)) + sqrt((cot x))] dx =

    A
    `pi/(sqrt2)`
    B
    `pi/(2sqrt(2))`
    C
    `(-(3 pi)/sqrt2)`
    D
    None

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