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 $\displaystyle 10^{-3}.$

Imayhave gotten it right, but does anyone have any ideas?

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- Dec 15th 2009, 08:44 AMAnonymous1estimate the integral
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? - Dec 15th 2009, 09:23 AMputnam120
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.

- Dec 15th 2009, 10:57 AMAnonymous1
That's what I did, only I'm not sure if my taylor expansion was right.

- Dec 15th 2009, 01:22 PMJester