The discussion revolves around a double integral problem, specifically focusing on the reversal of the order of integration. Participants are exploring the correct limits and anti-derivatives involved in the integration process.
Some participants have offered guidance on the correct anti-derivative for the integrand, while others suggest reconsidering the limits of integration. There appears to be a productive exploration of different approaches, though no explicit consensus has been reached.
There are indications of confusion regarding the treatment of functions in the context of integration, with references to common mistakes in calculus. The discussion also hints at reliance on computational tools for assistance with the integration process.
Yes, it is wrong. It is standard "Calculus I" mistake to treat a function of the variable as if it were just the variable but you should be past that by the time you are doing multiple integrals. "[itex]1/(1+ y^2)[/itex]" is NOT the same as [itex]1/y[/itex] and its anti-derivative is not a logarithm. The anti-derivative of [itex]1/(1+ y^2)[/itex] is [itex]arctan(y)+ C[/itex]. That's a standard anti-derivative that you should have memorized.emelie_earl said:
My idea was that the limits are
and that the anti-derivative of dy was
xlog(1+y^2)
but that seems wrong...
Yes, reversing the order of integration is the best way to handle this one. Integerating [itex]arctan(1)- arctan(x^2)= \pi/4- arctan(x^2)[/itex] is likely to be very difficult!maybe use these limits instead
and start with dx?
gives us
then we take dy
guess, i figured it out eventually with the help of wolfram with the last integration
Yes. I agree !HallsofIvy said: