# Math Help - Maclaurin's series question help

1. ## 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.

2. ## Re: Maclaurin's series question help

Write the series for the function under the integral and then integrate it.

3. ## 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!