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Math Help - Proving with Integration?

  1. #1
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    Proving with Integration?

    I was studying and I met the following problem:

    Prove that \int\sqrt{1-(a^2)(x^2)}(dx)= \sqrt{1-(a^2)} +\frac{\arcsin(a)}{a} for 0 < a < 1

    The integration has limits from -1 to 1. (Don't know how to show them with Latex ) And its in terms of x. (i.e: (dx))

    That "a" is causing me a lot of problems. If anyone can work out this proof for me so that I could retry it, I would deeply appreciate it.

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  2. #2
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    Quote Originally Posted by Tick View Post
    I was studying and I met the following problem:

    Prove that \int\sqrt{1-(a^2)(x^2)}(dx)= \sqrt{1-(a^2)} +\frac{\arcsin(a)}{a} for 0 < a < 1

    The integration has limits from -1 to 1. (Don't know how to show them with Latex ) And its in terms of x. (i.e: (dx))

    That "a" is causing me a lot of problems. If anyone can work out this proof for me so that I could retry it, I would deeply appreciate it.

     \int_{-1}^{1} \sqrt{1-a^2x^2} dx =  \int_{-1}^{1} \sqrt{a^2\bigg(\frac{1}{a^2}-x^2\bigg)} dx

     \int_{-1}^{1} a\sqrt{\bigg(\frac{1}{a}\bigg)^2 -x^2} dx  =  a\int_{-1}^{1} \sqrt{\bigg(\frac{1}{a}\bigg)^2 -x^2} dx

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  3. #3
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    Uh oh I got it, I got it! =D
    Thanks for the help Mush =]
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