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Trig substition confusion

  1. Oct 27, 2006 #1

    If I have the indefinite integral x(sqrt(4-x^2))dx

    must I replace x with 2sint and then dx = 2cosdt

    or can I just do regular substitution with u = 4-x^2 since xdx occurs in the integral already.

    when I solve it this way I get -1/3(4-x^2)^3/2 + C

    it just seems alot more work to do it the trigonometric substitituon way.

    Any help is much appreciated. Thanks!!
  2. jcsd
  3. Oct 27, 2006 #2
    you have to use the substitution [tex] x = 2\sin \theta [/tex].

    Thus [tex] dx = 2\cos \theta d\theta [/tex].

    At the end you have to solve for [tex] \theta [/tex] to convert the integral back in terms of x. you know that [tex] \sin \theta = \frac{x}{2} [/tex], so use a right triangle to express this relationship.
    Last edited: Oct 27, 2006
  4. Oct 27, 2006 #3

    are you positive? My professor Just emailed me saying that the substitution u = 4-x^2 is acceptable.

    Did you miss my x infront of the sqrt(4-x^2)dx ?

    Really confused now..
  5. Oct 27, 2006 #4


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    There is nothing wrong with your own substitution.
    You might check, though, that the two substitutions yield the same answer.
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