Line integral: $f(x,y)=g(\sqrt[3]{x^2+y^2})$

Question

I have to calculate line integral of curve $C=[R\cos{t},R\sin{t}],\;t\in\left<0,2\pi\right>$, and $f(x,y)=g(\sqrt[3]{x^2+y^2})$, where $R$ is real constant and $g$ is real function of one real variable.

I am confused, what should I do with $f(x,y)=g(\sqrt[3]{x^2+y^2})$. Thanks for help.

Answer 1

$$I=\int_Cf(x,y)dl=\int_Cg\left(\sqrt[3]{x^2+y^2}\right)dl$$ On the given curve $C$, you have $x^2+y^2=R^2$, so $$I=\int_Cg(R^{2/3})dl=g(R^{2/3})\int_C dl=2\pi R g(R^{2/3})$$