midpoint method of x^2-1 from 1 to 3 - Wolfram|Alpha

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Input interpretation:

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Result:

link to /input/?i=6.64&lk=1&a=ClashPrefs_*Math-
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Symbolic form of midpoint method:

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Plot:

Frame
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Exact result:

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Error vs. intervals:

Frame
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Method comparisons:

link to /input/?i=left+endpoint+method+++++++2+from+1.+to+3.+with+5+intervals%0A+++++++++++++++++++++-1+%2B+x&lk=1link to /input/?i=left+endpoint+method+++++++2+from+1.+to+3.+with+5+intervals%0A+++++++++++++++++++++-1+%2B+x&lk=1link to /input/?i=5.12&lk=1&a=ClashPrefs_*Math-link to /input/?i=1.54667&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.232&lk=1&a=ClashPrefs_*Math-link to /input/?i=right+endpoint+method+++++++2+from+1.+to+3.+with+5+intervals%0A++++++++++++++++++++++-1+%2B+x&lk=1link to /input/?i=right+endpoint+method+++++++2+from+1.+to+3.+with+5+intervals%0A++++++++++++++++++++++-1+%2B+x&lk=1link to /input/?i=8.32&lk=1&a=ClashPrefs_*Math-link to /input/?i=1.65333&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.248&lk=1&a=ClashPrefs_*Math-link to /input/?i=midpoint+method+++++++2+from+1.+to+3.+with+5+intervals%0A++++++++++++++++-1+%2B+x&lk=1link to /input/?i=6.64&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.0266667&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.004&lk=1&a=ClashPrefs_*Math-link to /input/?i=trapezoidal+rule+++++++2+from+1.+to+3.+with+5+intervals%0A+++++++++++++++++-1+%2B+x&lk=1link to /input/?i=trapezoidal+rule+++++++2+from+1.+to+3.+with+5+intervals%0A+++++++++++++++++-1+%2B+x&lk=1link to /input/?i=6.72&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.0533333&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.008&lk=1&a=ClashPrefs_*Math-link to /input/?i=Simpson%27s+rule+++++++2+from+1.+to+3.+with+5+intervals%0A+++++++++++++++-1+%2B+x&lk=1link to /input/?i=Simpson%27s+rule+++++++2+from+1.+to+3.+with+5+intervals%0A+++++++++++++++-1+%2B+x&lk=1link to /input/?i=6.66667&lk=1&a=ClashPrefs_*Math-link to /input/?i=Boole%27s+rule+++++++2+from+1.+to+3.+with+5+intervals%0A+++++++++++++-1+%2B+x&lk=1link to /input/?i=Boole%27s+rule+++++++2+from+1.+to+3.+with+5+intervals%0A+++++++++++++-1+%2B+x&lk=1link to /input/?i=6.66667&lk=1&a=ClashPrefs_*Math-
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Asymptotic expansion as the number of intervals goes to infinity:

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Mathematica input:

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Download full output as:

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