integrate using midpoint method x e^x - Wolfram|Alpha

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Input interpretation:

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Result:

link to /input/?i=35.8327&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++x+++from+-3.+to+3.+with+5+intervals%0A+++++++++++++++++++++E++x&lk=1link to /input/?i=left+endpoint+method++x+++from+-3.+to+3.+with+5+intervals%0A+++++++++++++++++++++E++x&lk=1link to /input/?i=13.4477&lk=1&a=ClashPrefs_*Math-link to /input/?i=26.9225&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.66689&lk=1&a=ClashPrefs_*Math-link to /input/?i=right+endpoint+method++x+++from+-3.+to+3.+with+5+intervals%0A++++++++++++++++++++++E++x&lk=1link to /input/?i=right+endpoint+method++x+++from+-3.+to+3.+with+5+intervals%0A++++++++++++++++++++++E++x&lk=1link to /input/?i=85.9349&lk=1&a=ClashPrefs_*Math-link to /input/?i=45.5647&lk=1&a=ClashPrefs_*Math-link to /input/?i=1.12867&lk=1&a=ClashPrefs_*Math-link to /input/?i=midpoint+method++x+++from+-3.+to+3.+with+5+intervals%0A++++++++++++++++E++x&lk=1link to /input/?i=35.8327&lk=1&a=ClashPrefs_*Math-link to /input/?i=4.53749&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.112397&lk=1&a=ClashPrefs_*Math-link to /input/?i=trapezoidal+rule++x+++from+-3.+to+3.+with+5+intervals%0A+++++++++++++++++E++x&lk=1link to /input/?i=trapezoidal+rule++x+++from+-3.+to+3.+with+5+intervals%0A+++++++++++++++++E++x&lk=1link to /input/?i=49.6913&lk=1&a=ClashPrefs_*Math-link to /input/?i=9.3211&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.230891&lk=1&a=ClashPrefs_*Math-link to /input/?i=Simpson%27s+rule++x+++from+-3.+to+3.+with+5+intervals%0A+++++++++++++++E++x&lk=1link to /input/?i=Simpson%27s+rule++x+++from+-3.+to+3.+with+5+intervals%0A+++++++++++++++E++x&lk=1link to /input/?i=40.4523&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.0820385&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.00203215&lk=1&a=ClashPrefs_*Math-link to /input/?i=Boole%27s+rule++x+++from+-3.+to+3.+with+5+intervals%0A+++++++++++++E++x&lk=1link to /input/?i=Boole%27s+rule++x+++from+-3.+to+3.+with+5+intervals%0A+++++++++++++E++x&lk=1link to /input/?i=40.3705&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.000233781&lk=1&a=ClashPrefs_*Math-link to /input/?i=5.79094x10%5E-6&lk=1&a=ClashPrefs_*Math-
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Mathematica input:

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Download full output as:

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