# Thread: Power series to find an integral

1. ## Power series to find an integral

Hello, I'm having trouble with the question below. I'm supposed to use a power series to approximate this integral, but the way I tried it seemed to fail horribly. Does anybody know how to do this?

Use a power series to approximate the definite integral to six decimal places.

What I tried was to take the derivative, then make a power series for that, and then integrate that summation twice. That's most likely wrong, but I'm not sure why. Any help would be appreciated.

Thank you

2. Originally Posted by bnay
Hello, I'm having trouble with the question below. I'm supposed to use a power series to approximate this integral, but the way I tried it seemed to fail horribly. Does anybody know how to do this?

Use a power series to approximate the definite integral to six decimal places.

What I tried was to take the derivative, then make a power series for that, and then integrate that summation twice. That's most likely wrong, but I'm not sure why. Any help would be appreciated.

Thank you
Note that $\ln (1 + x) = \sum_{n = 1}^\infty (-1)^{n+ 1}\frac {x^n}n$ for $|x| \le 1$, $x \ne -1$

now replace $x$ with $x^5$ everywhere, then integrate term by term