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Trigonometric substitutions

  1. Jul 23, 2010 #1
    I received the following email:
    I can't see the logic in assuming (for example) that a function containing sqrt (a^2 - x^2) in the integrand would lead you to substitute x with a trig reference. Why a trig reference? What connection does the integrand, trig-less function have to trigonometry? To me, it seems about as rational as replacing the 'a' with pi, or e, or a sausage!
    How can I make this tangible?
    Are there any online illustrations of this?
  2. jcsd
  3. Jul 24, 2010 #2
    Let him substitute x=a cos(t) and see for himself. Remember sin^2(t)+cos^2(t)=1. The squares in this equation are the link to square roots.
    It's pretty self-explanatory once you've actually tried it out.
  4. Jul 25, 2010 #3
    I know what he means.

    Tell him that integrand is related to a circle which is related to a trig function (and related to pi)
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