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Math Help - [SOLVED] Trig Subst

  1. #1
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    [SOLVED] Trig Subst

    Ok I know you have to do trig substitution but its been awhile since I've done so : /

    The problem is : The integral of 2Sqrt(1-x^2)
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    Quote Originally Posted by Link88 View Post
    Ok I know you have to do trig substitution but its been awhile since I've done so : /

    The problem is : The integral of 2Sqrt(1-x^2)

    I think if \sqrt{a^2 -x^2} occurs in an integrand, you have to try the substitution x=a sin \theta. In this case a=1.

    EDIT: I will show you one more step:

    Since x=a sin \theta implies that \theta = sin^{-1} x
    Therefore, dx = cos \theta d \theta. Can you continue from here?
    Last edited by Roam; November 28th 2009 at 07:25 PM.
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  3. #3
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    Quote Originally Posted by Roam View Post
    Why would you want a trig substitution? Does re-writing it as \int 2(1-x^2)^{\frac{1}{2}} dx help?
    I'm not sure what you have in mind but no, this doesn't help.

    A trig substitution is required. One possible choice is x = \sin t.

    @OP: If you need more help, please show all your working and say where it is that you get stuck.
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    The original posted question was wrong. See here: http://www.mathhelpforum.com/math-he...tml#post413788

    This thread is being kept open in case other members want to follow up on the posted question.
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    Ok I'll brush up a bit on trig. subst.
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  6. #6
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    ah ha! got it!

    sin^-1(x) +(1 - x^2)^1/2 + c

    The trick is to pull the 2 in front of the integral before you start and let x = sinx and go from there! ok thanks! : )
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  7. #7
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    Quote Originally Posted by Link88 View Post
    ah ha! got it!

    sin^-1(x) +(1 - x^2)^1/2 + c

    The trick is to pull the 2 in front of the integral before you start and let x = sinx and go from there! ok thanks! : )
    You might find this website useful: - Wolfram|Alpha

    Be sure to click on Show steps.
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