## anonymous one year ago Help please!!! Using Simpson's rule Determine the upper bound on the error in the following integral. Open to see it because i cant write equations in the top part of the question

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1. anonymous

$\int\limits_{1}^{3}(\sqrt[4]{X^2+1})$

2. anonymous

This will be useful: https://en.wikipedia.org/wiki/Simpson%27s_rule#Error

3. anonymous

This means you'll have to find the upper bound of the fourth derivative of your given function. \begin{align*} f(x)&=(x^2+1)^{1/4}\\\\ f'(x)&=\frac{2x}{(x^2+1)^{3/4}}\\\\ f''(x)&=\frac{4x^2-3x+4}{2(x^2+1)^{7/4}}\\\\ f''''(x)&=\frac{-12x^3+15x^2-12x-6}{4(x^2+1)^{11/4}} \end{align*} (Check those derivatives, it's possible I made some mistake in the derivations)

4. anonymous

Definitely some mistakes...

5. anonymous

hmmm ya

6. mathmate

Correction: See also : http://openstudy.com/study#/updates/55a1e417e4b05670bbb52311 where $$f^{iv}(x)$$ is given.

7. anonymous

eh I'm too lazy to solve it bai :3 btw the asker isn't here

8. anonymous

Hmm same problem, that's convenient :P

9. anonymous

xD ima help the guy with the salmon question