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# Calculate 3rd order iterated integral with bounds in Wolfram|Alpha?

Posted 8 years ago
 Why does Wolfram Alpha website flip the second and third bounds on this 3rd order iterated integral? The order of multi-variable integration is important when the bounds are not constant. I typed integral of xyz from z = 1 to y, y = -1 to x^2, x = 0 to 2 into the website computation bar, but Wolfram took the integral with respect to z, then x then y and gave the answer 1/4(x^4-1)^2. Link to this search. Typing integral of xyz from z = 1 to y, x = 0 to 2, y = -1 to x^2 (flipping x and y) gave the output I expected from the first search: 10.3833 Link to this search. This bug isn't very critical because Wolfram consistently switches the bounds, but does anyone know why this happens?
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Posted 8 years ago
 I agree, and will look into it. In the meantime, if you specify dzdydx right after the xyz, alpha will integrate the expression in that order.
Posted 8 years ago
 I do not know but I agree it is problematic. Will report.
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