I would like to complete the surface integral $\int\int x^2y^2dxdy$ bound by the triangle $y=4x$, $y=0$, $x=1$ integrating over y first. I can do the integral itself, however, I'm unsure of what limits to choose at each stage


1 Answer 1


If you invert the integral using the Frobenius Theorem you trivially get $$\int_{0}^{1} \int_{0}^{4x} x^2y^2dydx$$

  • $\begingroup$ thank you. and what if you integrate over x first? $\endgroup$
    – MA98765
    Nov 7, 2021 at 22:50
  • $\begingroup$ When $x\in(0,1), y\in $what? And when $y=4x, x=$what? $\endgroup$ Nov 7, 2021 at 22:52

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