Plotting the integration domain for integration borders clarityLUkvaW1wbGljaXRwbG90M2RHNiI2KTcmL0kieEdGJCIiIS9JInlHRiRGKS9JInpHRiRGKS9GLS1JIitHJSpwcm90ZWN0ZWRHNiQiIiIsJkYoISIiRitGNS9GKDtGKUYzL0YrRjcvRi1GNy9JJWF4ZXNHRiRJJmJveGVkR0YkL0ktdHJhbnNwYXJlbmN5R0YkNyYkIiIpRjVGQCQiIiRGNUZCL0ksb3JpZW50YXRpb25HRiQ3JCEjdiIjdg==%;JSFHJSFHQyg+JkkiUkc2IjYjSSJ4R0YmOyIiISIiIiEiIj4mRiU2I0kieUdGJjtGKiwmRitGK0YoRixGLD4mRiU2I0kiekdGJjtGKi1JIitHJSpwcm90ZWN0ZWRHNiRGKywmRihGLEYwRixGLA==print(); # input placeholderJSFHLUkkaW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtRiM2JC1GIzYkSSJ4R0YnL0kiekdGJzsiIiEtSSIrR0YlNiQiIiIsJkYtISIiSSJ5R0YnRjcvRjg7RjEsJkY1RjVGLUY3L0YtO0YxRjU= = print(); # input placeholderJSFHJSFHJSFH
JSFH%;One interesting thing to note is that due to the very special shape of this domain, integration order is totally irrelevant! One simple way ot show that is by trading axes, without changing the integration borders (which is an equivalent to rotating the reference frame and integraton order), e.g.: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 = print(); # input placeholderJSFHJSFHJSFHJSFHJSFHJSFHJSFH