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Math Help - understanding trig. substitution

  1. #1
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    understanding trig. substitution

    http://www.mathhelpforum.com/math-he...-4-x-2-dx.html

    hi,

    can anyone explain why sub X = 2 sin (theta) ?
    Last edited by Krizalid; March 14th 2009 at 12:15 PM.
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  2. #2
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    Quote Originally Posted by Chris0724 View Post
    why sub x = 2 sin (theta) ?
    Inorder to do it by integration by substitution

    -Have you read the complete thread?

    -What's the main question you have?

    ---------------------------------------------
    --If it is that we can substitute this directly in the formula
    ----than the formula is also derived like this
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    hi,

    i understand that in order for the substitution to work, we have to sub in x = 2 sin (theta)

    but is there any other term that will work other than 2 sin (theta) ?

    How do we know, by looking at the qns, we have to sub in 2 sin theta ?

    thanks!
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  4. #4
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    It's just a matter of manipulating it to use certain trigonometric identities.

    If your integrand contains something of the form:
    • \sqrt{a^2 - x^2} use x = a\sin \theta so you can use the identity: 1 - \sin^2 \theta = \cos \theta
    • \sqrt{x^2 - a^2} use x = a\sec \theta so you can use the identity: \sec^2 \theta - 1 = \tan \theta
    • \sqrt{a^2 + x^2} use x = a\tan \theta so you can use the identity: 1 + \tan^2 \theta = \sec^2 \theta


    The question posed in this thread is an example of the first.
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  5. #5
    Moo
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    Or if you've dealt with hyperbolic trigonometry, you can use this identity : \cosh^2(x)-\sinh^2(x)=1

    So if you have \sqrt{a^2+x^2}, you can substitute x=a \sinh(t) and hence \sqrt{a^2+x^2}=a \cosh(t)
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