Just got out of my Analysis final and one of the questions was: Estimate $\displaystyle f(x) = \int_0^1 \sin(x^2)dx$ to within $\displaystyle 10^{-3}.$ I may have gotten it right, but does anyone have any ideas?
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I would probably have expanded $\displaystyle \sin (x^2)$ with a Taylor series and then integrated term by term (since the convergence is uniform). Though how many terms I am not quite sure.
That's what I did, only I'm not sure if my taylor expansion was right.
Originally Posted by Anonymous1 That's what I did, only I'm not sure if my taylor expansion was right. $\displaystyle \sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} \pm \cdots $ BTW - you only need two terms.
Last edited by Jester; Dec 15th 2009 at 01:26 PM. Reason: Added a note
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