Solve integral $$\iint_{x^2+y^2<\sqrt{x}}\sqrt{x^2+y^2}dxdy$$
I was thinking about substitution $(x,y)\mapsto(t^2,y)$ but I do not think this is efficient way to solve it.
2026-04-11 16:50:53.1775926253
Solve integral $\iint_{x^2+y^2<\sqrt{x}}\sqrt{x^2+y^2}dxdy$
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You are right. Polar coordinates are the way to go with this integral. A general hint: Whenever you see something of the form: $x^2 +y^2$, immediately think about polar coordinates.
The answer is $\frac{2}{3}$, as you calculated correctly. Well done!