# Math Help - maclaurin series with radical integral

1. ## maclaurin series with radical integral

I am trying to get the first four terms of the Maclaurin Series for the following functiong:

integral from 0 to x of sqrt(1+t^3) dt

Sadly, I'm stuck trying to find the integral so that I can get the first f(0) term. Using u-substitution I get:

u = 1 + t^3
du = 3t^2 dt
dt= du / 3t^2

I think that I need to put 3t^2 in terms of u to be able to continue with the integration, but I cannot see a connection. If I make u = t^3 then would 3t^2 = 3u^2/3 ??

thanks!

2. ## hello again

remember any integral from 0 to 0 or in fact a to a is 0.

No one can do the integral

3. Hi

The Maclaurin series of f is $\sum_{n=0}^{+\infty} \frac{f^{(n)}(0)}{n!}\:x^n$

$f(0) = 0$

$f'(x) = \sqrt{1+x^3} \implies f'(0) = 1$

You can show that $f^{(2)}(0) = 0$ and $f^{(3)}(0) = 0$

Spoiler:
Therefore the first four terms of the Maclaurin Series is ... $x$