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Math Help - Show that Int(1,infinity,sin(x^2)) converges

  1. #1
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    Show that Int(1,infinity,sin(x^2)) converges

    I need to show that integral of sin(x^2) from 1 to infinity converge

    The only hint I have is "Let y=x^2". I did a change of variable at first and an integration by parts, but now I'm stuck. Does anyone can help me.

    Thanks
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Show that Int(1,infinity,sin(x^2)) converges

    Quote Originally Posted by solvj View Post
    The only hint I have is "Let y=x^2". I did a change of variable at first and an integration by parts, but now I'm stuck.
    Good, now use \left|\int_a^bf(x)\;dx\right|\leq \int_a^b|f(x)|\;dx and the fact that \int_1^{+\infty}\dfrac{dt}{t^{3/2}} is convergent.
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  3. #3
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    Re: Show that Int(1,infinity,sin(x^2)) converges

    Thank you, that completes my proof.
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