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

Questions
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1

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?

2

I do not know but I agree it is problematic. Will report.

3

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.