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?