# Maclaurin's series question help

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• Jan 14th 2013, 05:21 AM
tempq1
Maclaurin's series question help
Use the relationship
$\displaystyle \int \frac{1}{\sqrt{1-x^2}}\ dx = \arcsin x + C$
to find the first four nonzero terms in the Maclaurin's series for $\displaystyle arcsinx$.
I don't have any idea on how to relate them together. thanks in advance.
• Jan 14th 2013, 05:35 AM
emakarov
Re: Maclaurin's series question help
Write the series for the function under the integral and then integrate it.
• Jan 14th 2013, 05:35 AM
Barioth
Re: Maclaurin's series question help
Hi

With the information you gave us, we know that

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

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

so what we're missing now are $\displaystyle f''(x), f^{(3)}(x),$ 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!