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Thread: estimate the integral

  1. December 15th 2009, 09:44 AM #1
    Anonymous1
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    estimate the integral

    Just got out of my Analysis final and one of the questions was:

    Estimate f(x) = \int_0^1 \sin(x^2)dx to within 10^{-3}.

    I may have gotten it right, but does anyone have any ideas?
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  2. December 15th 2009, 10:23 AM #2
    putnam120
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    I would probably have expanded \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.
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  3. December 15th 2009, 11:57 AM #3
    Anonymous1
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    That's what I did, only I'm not sure if my taylor expansion was right.
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  4. December 15th 2009, 02:22 PM #4
    Danny
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    Quote Originally Posted by Anonymous1 View Post
    That's what I did, only I'm not sure if my taylor expansion was right.
    <br /> \sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} \pm \cdots<br /> BTW - you only need two terms.
    Last edited by Danny; December 15th 2009 at 02:26 PM. Reason: Added a note
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