# Thread: Error Bounds

1. ## Error Bounds

How large should n be to guarantee that the Simpson's Rule approximation to the integral of 0 to 1 of e^(x^2) is accurate to within 0.00001?

so I took the function up to it's 4th derivative.
how am i supposed to find k?
stupid teacher did not clearly tell us how to find it and this book (Stewart's) i heard was not clear either.

2. Originally Posted by xfyz
stupid teacher did not clearly tell us how to find it and this book (Stewart's) i heard was not clear either.
You may wish to lose this attitude. It is possible both the teacher and the author want you to learn how to think.

The error term for Simpson's Rule is $\displaystyle \frac{1}{90}f^{4}(c)h^{5}$. Your task is to find where this expression MUSt be less than 0.00001.

Well, $\displaystyle \frac{1}{90}f^{4}(c)h^{5} < 0.00001$

$\displaystyle f^{4}(c)h^{5} < 0.00090$

It's a little tricky, right here. This requires some judgment. Where on your interval is the fourth derivative GREATEST? If we find where it is greatest, we can guarantee the error will be as desired. Find the value of 'c' that maximizes the fourth derivative. Evaluate that derivative. Substitute in the inequality and finish solving for 'h'. This can be translated into the appropriate value of 'n' that is required.

Let's see what you get.