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Math Help - Maclaurin's series question help

  1. #1
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    Maclaurin's series question help

    Use the relationship
    \int \frac{1}{\sqrt{1-x^2}}\ dx = \arcsin x + C
    to find the first four nonzero terms in the Maclaurin's series for arcsinx.
    I don't have any idea on how to relate them together. thanks in advance.
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  2. #2
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    Re: Maclaurin's series question help

    Write the series for the function under the integral and then integrate it.
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  3. #3
    Junior Member Barioth's Avatar
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    Re: Maclaurin's series question help

    Hi

    With the information you gave us, we know that

     f(x) = \arcsin(x) \ \\ f'(x) = \frac{1}{\sqrt{1-x^2}}

    A maclaurin series is
     f(x) = f(0) +f'(0)\frac{x^1}{1!}+f''(0)*\frac{x^2}{2!}+...+f^{  (n)}*\frac{x^{(n)}}{(n!)}

    so what we're missing now are  f''(x), f^{(3)}(x), etc. witch is up to you do find!

    Remember you only have to find the first 4 that are non equal to 0.

    Hope that helped, if not let me know!
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