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calculus II

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Using integration by substitution.
find the exact value of

integral from [0,9/16]
sqrt(1 - sqrt(x))/(sqrt(x))

  • calculus II -

    Do a u substitution.

    u= 1- sqrt(x)
    du = -(1/(2*sqrt(x)))dx

    Change your limits by plugging them into the u equation.

    u= 1 - sqrt(0) = 1-0 = 1
    u= 1 - sqrt(9/16) = 1-(3/4) = 1/4

    Substitute the u values in for x.

    The new integral is -2*sqrt(u) du from [1,1/4]

    OR

    2*sqrt(u) du from [1/4,1]


    You integrate and get 2*(2/3)*u^(3/2) evaluated from [1/4,1]. Plug in 1, then plug in (1/4). Subtract these two values and you should get your answer.

    I got 7/6 or 1.166667

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