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Math Help - Double Integral question

  1. #1
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    Double Integral question

    Hey everyone, I'm having some trouble in my Multivariable Calculus class. I hope someone can help! I'm sorry that I don't know how to properly make the integral look pretty! Thanks in advance.

    Integral(Integral(sin(x^2))dx)dy

    the limits are y < x < 3, 0 < y < 3.

    Wolfram gives me an answer of 0.955565, but I'd love to know how it came up with this.
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  2. #2
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    There isn't an elementary anti-derivative of \sin(x^2) as far as I know. Wolfram may have used a numerical integration technique, such as the Trapezoidal Rule, to approximate the integral.
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  3. #3
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by NOX Andrew View Post
    There isn't an elementary anti-derivative of \sin(x^2) as far as I know. Wolfram may have used a numerical integration technique, such as the Trapezoidal Rule, to approximate the integral.
    True, but this is a double integral and we can change the bounds to find a possible solution.

     \int_0^3 \int_y^3 sin x^2 dxdy = \int_0^3 \int_0^x sin x^2 dydx = \int_0^3 sin x^2 dx \int_0^x dy = \int_0^3 xsin x^2 dx

    And we can now solve that without any trouble!
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  4. #4
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    Quote Originally Posted by AllanCuz View Post
    True, but this is a double integral and we can change the bounds to find a possible solution.

     \int_0^3 \int_y^3 sin x^2 dxdy = \int_0^3 \int_0^x sin x^2 dydx = \int_0^3 sin x^2 dx \int_0^x dy = \int_0^3 xsin x^2 dx

    And we can now solve that now without any trouble!
    Right! Fubini's Theorem! Thanks!
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