# Newton's Binomial Theorem to Estimate, Find Error

1. Jul 22, 2011

### jillian3

1. The problem statement, all variables and given/known data

Use Newton's Binomial Theorem to estimate integral of (1+x^4)^(1/2) from 0 to 1/2 to within one part in 1000, (error>1/1000)

2. Relevant equations

I used the Binomial Series expansion, so (a+b)^n = a^n +na^(n-1)b + (n(n-1))/2! (etc

3. The attempt at a solution

I understand how to do a binomial series expansion, but I don't know how to use it to estimate a value and find the error in this case. I'm using the series expansion to estimate a value for integral given. So I need to add up several of the functions in the series expansion, subtract it from the value for the integral of (1+x^4)^(1/2) from 0 to 1/2. But the value of this is not an exact number, and I can't put it in a format of (1+x) and plug in for my expansion to get values.

First off, is this how you use the theorum to estimate? Is that how you find the error? And if that is the case, how d I find the error or estimate with the information i'm given?