integrate x cos x from 1 to 3 with left endpoint method - Wolfram|Alpha
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Input interpretation:

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Result:

link to /input/?i=-1.26133&lk=1&a=ClashPrefs_*Math-
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Symbolic form of left endpoint 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+Cos%5Bx%5D+from+1.+to+3.+with+5+intervals&lk=1link to /input/?i=left+endpoint+method+x+Cos%5Bx%5D+from+1.+to+3.+with+5+intervals&lk=1link to /input/?i=-1.26133&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.687077&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.352636&lk=1&a=ClashPrefs_*Math-link to /input/?i=right+endpoint+method+x+Cos%5Bx%5D+from+1.+to+3.+with+5+intervals&lk=1link to /input/?i=right+endpoint+method+x+Cos%5Bx%5D+from+1.+to+3.+with+5+intervals&lk=1link to /input/?i=-2.66544&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.717034&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.368011&lk=1&a=ClashPrefs_*Math-link to /input/?i=midpoint+method+x+Cos%5Bx%5D+from+1.+to+3.+with+5+intervals&lk=1link to /input/?i=-1.94086&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.00754533&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.00387257&lk=1&a=ClashPrefs_*Math-link to /input/?i=trapezoidal+rule+x+Cos%5Bx%5D+from+1.+to+3.+with+5+intervals&lk=1link to /input/?i=trapezoidal+rule+x+Cos%5Bx%5D+from+1.+to+3.+with+5+intervals&lk=1link to /input/?i=-1.96338&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.0149785&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.00768755&lk=1&a=ClashPrefs_*Math-link to /input/?i=Simpson%27s+rule+x+Cos%5Bx%5D+from+1.+to+3.+with+5+intervals&lk=1link to /input/?i=Simpson%27s+rule+x+Cos%5Bx%5D+from+1.+to+3.+with+5+intervals&lk=1link to /input/?i=-1.94837&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.0000373993&lk=1&a=ClashPrefs_*Math-link to /input/?i=0.0000191948&lk=1&a=ClashPrefs_*Math-link to /input/?i=Boole%27s+rule+x+Cos%5Bx%5D+from+1.+to+3.+with+5+intervals&lk=1link to /input/?i=Boole%27s+rule+x+Cos%5Bx%5D+from+1.+to+3.+with+5+intervals&lk=1link to /input/?i=-1.94841&lk=1&a=ClashPrefs_*Math-link to /input/?i=1.54237x10%5E-8&lk=1&a=ClashPrefs_*Math-link to /input/?i=7.91607x10%5E-9&lk=1&a=ClashPrefs_*Math-
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Mathematica input:

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