Use the Taylor polynomial of degree up to 3 for y = cos x along with Taylor's inequality to estimate (integral from 0 to 1) of cos(x^2) and give a bound on the error that your estimate makes.

I'm not quite sure how to do this.

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- Mar 28th 2010, 09:16 PMcrymorenoobsTaylor's inequality problem
Use the Taylor polynomial of degree up to 3 for y = cos x along with Taylor's inequality to estimate (integral from 0 to 1) of cos(x^2) and give a bound on the error that your estimate makes.

I'm not quite sure how to do this. - Mar 28th 2010, 10:21 PMAnonymous1

Also, you need to find the remainder term to find the bound on error. You know... - Mar 28th 2010, 10:33 PMcrymorenoobs
Ok thank you, I don't know why the integral threw me off...seems straight forward enough :).

- Mar 28th 2010, 10:41 PMcrymorenoobs
Incase anyone else is interested in this answer in the future, the x^8 term should not be included (since it is of degree 3 and the x^4 term isn't used). Thanks again for the reply though.

- Mar 28th 2010, 11:02 PMAnonymous1
Yes, this is correct. Note that if you want to use the order expansion, which is what I implied with

I've edited the post to show we are finding an