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Evaluating difficult integral involving square roots

  1. Mar 24, 2013 #1
    1. The problem statement, all variables and given/known data
    Evaluate the following integral

    2. Relevant equations
    ∫ √(4-(√x)) dx

    3. The attempt at a solution
    I am having a mind block, I find this too challenging, help!!
  2. jcsd
  3. Mar 24, 2013 #2


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    Well, the instant I look at that I think of setting [itex]u= 4- \sqrt{x}= 4- x^{1/2}[/itex]. Then [itex]du= -(1/2)x^{-1/2}dx[/itex] so that [itex]dx= -2x^{1/2}du= -2\sqrt{x}du[/itex].

    And, since [itex]u= 4- \sqrt{x}[/itex], [itex]\sqrt{x}= 4- u[/itex].
  4. Mar 24, 2013 #3
    I understand the du = ... But what happens to the square root of the entire function?
  5. Mar 24, 2013 #4
    That's the whole point of setting ##u = 4 - \sqrt{x}##, the integral then becomes ##\int \sqrt{u} \ (2u-8) \ du ##, you simply substitute u in for ##4 - \sqrt{x}##.

    There are other ways of solving this integral as well. You can use trig substituion and you can also set ##u^2 = 4 - \sqrt{x}## and still arrive at the correct result.
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