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Math Help - Numerical integration?

  1. #1
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    Numerical integration?

    I am having difficulty integrating

    square root((1+x^3)) from x=0 to x=2

    when n=4

    I know the widths are 0,1/2,1,3/2,2

    But I am having trouble setting it up.
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  2. #2
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    Re: Numerical integration?

    Quote Originally Posted by homeylova223 View Post
    I am having difficulty integrating

    square root((1+x^3)) from x=0 to x=2 when n=4
    Let f(x)=\sqrt{1+x^2} and \Delta=0.5.

    Left hand sum \sum\limits_{k = 0}^3 {f\left( {k\Delta } \right)\Delta } .

    Right hand sum \sum\limits_{k = 1}^4 {f\left( {k\Delta } \right)\Delta } .


    Mid-point hand sum \sum\limits_{k = 0}^3 {f\left( {\frac{2k\Delta+\Delta }{2} \right)\Delta } .
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  3. #3
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    Re: Numerical integration?

    I forgot to mention I have to use the trapezoid rule and I set it up like this.

    ((2/8)) times (1)(1+(0)^3)+(2)(1+(1/2)^3)+(2)(1+(1)^3)+(2)(1+(3/2)^3)+(1)(1+(2)^(3)
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Numerical integration?

    It looks fine if you don't forget to take the square root of the seperated terms because f(x)=\sqrt{1+x^3}.
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  5. #5
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    Re: Numerical integration?

    Thanks now I see the error of my calculus.
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Numerical integration?

    You're welcome!
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