using Simpson's rule integrate Bessel J(2,x)/(1 + x^2) from 1 to 3 with 10 intervals - Wolfram|Alpha

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Input interpretation:

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    Result:

    link to /input/?i=0.129837&lk=1&a=ClashPrefs_*Math-
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    Symbolic form of Simpson's rule:

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    Plot:

    Frame
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    Exact result:

    link to /input/?i=0.129836&lk=1&a=ClashPrefs_*Math-
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    Method comparisons:

    link to /input/?i=left+endpoint+method+BesselJ%5B2%2C+x%5D+from+1.+to+3.+with+10+intervals%0A+++++++++++++++++++++-------------%0A+++++++++++++++++++++++++++++2%0A++++++++++++++++++++++++1+%2B+x&lk=1link to /input/?i=left+endpoint+method+BesselJ%5B2%2C+x%5D+from+1.+to+3.+with+10+intervals%0A+++++++++++++++++++++-------------%0A+++++++++++++++++++++++++++++2%0A++++++++++++++++++++++++1+%2B+x&lk=1link to /input/?i=0.13047&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.000633123&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.00487631&lk=1&a=ClashPrefs_*Math-link to /input/?i=right+endpoint+method+BesselJ%5B2%2C+x%5D+from+1.+to+3.+with+10+intervals%0A++++++++++++++++++++++-------------%0A++++++++++++++++++++++++++++++2%0A+++++++++++++++++++++++++1+%2B+x&lk=1link to /input/?i=right+endpoint+method+BesselJ%5B2%2C+x%5D+from+1.+to+3.+with+10+intervals%0A++++++++++++++++++++++-------------%0A++++++++++++++++++++++++++++++2%0A+++++++++++++++++++++++++1+%2B+x&lk=1link to /input/?i=0.128701&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.0011354&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.00874485&lk=1&a=ClashPrefs_*Math-link to /input/?i=midpoint+method+BesselJ%5B2%2C+x%5D+from+1.+to+3.+with+10+intervals%0A++++++++++++++++-------------%0A++++++++++++++++++++++++2%0A+++++++++++++++++++1+%2B+x&lk=1link to /input/?i=0.129962&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.000125576&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.000967186&lk=1&a=ClashPrefs_*Math-link to /input/?i=trapezoidal+rule+BesselJ%5B2%2C+x%5D+from+1.+to+3.+with+10+intervals%0A+++++++++++++++++-------------%0A+++++++++++++++++++++++++2%0A++++++++++++++++++++1+%2B+x&lk=1link to /input/?i=trapezoidal+rule+BesselJ%5B2%2C+x%5D+from+1.+to+3.+with+10+intervals%0A+++++++++++++++++-------------%0A+++++++++++++++++++++++++2%0A++++++++++++++++++++1+%2B+x&lk=1link to /input/?i=0.129585&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.000251138&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.00193427&lk=1&a=ClashPrefs_*Math-link to /input/?i=Simpson%27s+rule+BesselJ%5B2%2C+x%5D+from+1.+to+3.+with+10+intervals%0A+++++++++++++++-------------%0A+++++++++++++++++++++++2%0A++++++++++++++++++1+%2B+x&lk=1link to /input/?i=Simpson%27s+rule+BesselJ%5B2%2C+x%5D+from+1.+to+3.+with+10+intervals%0A+++++++++++++++-------------%0A+++++++++++++++++++++++2%0A++++++++++++++++++1+%2B+x&lk=1link to /input/?i=0.129837&lk=1&a=ClashPrefs_*Math-link to /input/?i=4.55793x10%5E-9&lk=1&a=ClashPrefs_*Math-link to /input/?i=3.51052x10%5E-8&lk=1&a=ClashPrefs_*Math-link to /input/?i=Boole%27s+rule+BesselJ%5B2%2C+x%5D+from+1.+to+3.+with+10+intervals%0A+++++++++++++-------------%0A+++++++++++++++++++++2%0A++++++++++++++++1+%2B+x&lk=1link to /input/?i=Boole%27s+rule+BesselJ%5B2%2C+x%5D+from+1.+to+3.+with+10+intervals%0A+++++++++++++-------------%0A+++++++++++++++++++++2%0A++++++++++++++++1+%2B+x&lk=1link to /input/?i=0.129836&lk=1&a=ClashPrefs_*Math-link to /input/?i=6.77491x10%5E-11&lk=1&a=ClashPrefs_*Math-link to /input/?i=5.21804x10%5E-10&lk=1&a=ClashPrefs_*Math-
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    Mathematica input:

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