# Boundaries change in double integral

Calculate: $$\int_0^1 \int_0^{x^3} e^\frac{y}{x} dydx$$ Obviously i need to change it to $dxdy$ thus i need to change the boundaries of the second integral but how to do that in this case?

• I think you'll find this problem more difficult if you switch the order of integration – jameselmore Aug 20 '15 at 14:39
• Boundaries are fine. – Anthony Aug 20 '15 at 14:40
• Thus should i use polar coordinates in this integral or just leave it as it is? – mkropkowski Aug 20 '15 at 14:42
• As is. It's fairly straightforward, although it looks complicated. – Daniel Fischer Aug 20 '15 at 14:45

As presented the integral may be best suited. By integrating $y$ first makes $x$ a "constant" in that particular integral. Alternatively if $x$ is is integrated first a change of variable will need to be made, ie $x \to \frac{1}{t}$ as well as changing the integration limits.