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int0^(pi//2)(sqrt(sin x))/(sqrt(sin x) +...

`int_0^(pi//2)(sqrt(sin x))/(sqrt(sin x) + sqrt(cos x)) dx` equals:

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The correct Answer is:
(b) 3/4
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Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (c) int_(0)^(pi/2)(sqrt(sinx))/(sqrt(sin x) + sqrt(cos x))dx

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Knowledge Check

  • int_0^(pi//2) (3^(sin x))/(3^(sin x) + 3^(cos x)) dx equals :

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

  • int (sqrt(tan x) + sqrt(cot x)) dx is equal to

    A
    `sin^(-1)(sin x-cos x)+c`
    B
    `sqrt 2 sin^(-1) (sin x-cosx) + c`
    C
    `sqrt 2 cos^(-1) (sin x-cosx) + c`
    D
    none of these

  • int_0^(pi//2) (sqrt( cot x))/(sqrt(cot x) - sqrt(tan x)) dx is :

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

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    int (sin 5x)/(sqrt(cos 5x)) dx =

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    int_0^(pi/4) (sqrt tanx)/(sin x cos x) dx =

    int_0^(pi//2) (sin x + cos x)/(sqrt(1 + sin 2x)) dx is :

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