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Math Help - More Simpson Rule Question

  1. #1
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    More Simpson Rule Question

    Hi

    The following question i don't know why it is incorrect.
    1) \int_1^3 x^{x}dx n=4

    x_0 = 0

    x_1 = \frac{1}{4}

    x_2 = \frac{2}{4}

    x_3 = \frac{3}{4}

    x_4 = \frac{4}{4}

    \int_0^1 x^{x} dx = \frac{1}{12}[0+4(\frac{1}{4}^{\frac{1}{4}})+2(\frac{1}{2}^{\fra  c{1}{2}})+4(\frac{3}{4}^{\frac{3}{4}})+1]

    =0.70553

    book's answer is 0.7889
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Paymemoney View Post
    Hi

    The following question i don't know why it is incorrect.
    1) \int_1^3 x^{x}dx n=4

    x_0 = 0

    x_1 = \frac{1}{4}

    x_2 = \frac{2}{4}

    x_3 = \frac{3}{4}

    x_4 = \frac{4}{4}

    \int_0^1 x^{x} dx = \frac{1}{12}[0+4(\frac{1}{4}^{\frac{1}{4}})+2(\frac{1}{2}^{\fra  c{1}{2}})+4(\frac{3}{4}^{\frac{3}{4}})+1]

    =0.70553

    book's answer is 0.7889
    Why have you used 0^0=0 in this case? You need \lim_{x \to 0}x^x=1

    Next time you post a question try to make it clear what your question is, and don't change the detail part way through.

    CB
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  3. #3
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    Quote Originally Posted by Paymemoney View Post
    Hi

    The following question i don't know why it is incorrect.
    1) \int_0^1 x^{x}dx n=4

    x_0 = 0

    x_1 = \frac{1}{4}

    x_2 = \frac{2}{4}

    x_3 = \frac{3}{4}

    x_4 = \frac{4}{4}

    \int_0^1 x^{x} dx = \frac{1}{12}[0+4(\frac{1}{4}^{\frac{1}{4}})+2(\frac{1}{2}^{\fra  c{1}{2}})+4(\frac{3}{4}^{\frac{3}{4}})+1]

    =0.70553

    book's answer is 0.7889
    srry about that, the above is the correct equation.
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  4. #4
    Grand Panjandrum
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    \int_0^1 x^{x} dx = \frac{1}{12}[1+4(\frac{1}{4}^{\frac{1}{4}})+2(\frac{1}{2}^{\fra  c{1}{2}})+4(\frac{3}{4}^{\frac{3}{4}})+1]

    =0.7889
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  5. #5
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    Quote Originally Posted by CaptainBlack View Post
    \int_0^1 x^{x} dx = \frac{1}{12}[1+4(\frac{1}{4}^{\frac{1}{4}})+2(\frac{1}{2}^{\fra  c{1}{2}})+4(\frac{3}{4}^{\frac{3}{4}})+1]

    =0.7889
    but isn't x_0 equal to 0?
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by Paymemoney View Post
    but isn't x_0 equal to 0?
    No that's why I said it's not in post #2 in this thread. 0^0 is undefined here you need to use \lim_{x\to 0}x^x=1 for the value of the integrand at x=0

    CB
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