Let
$$C = \left\{ (x,y,z)\in\mathbb{R}^3 \mid x^2+y^2 = {25}, z = 0 \right\}.$$
I want to integrate
$$\displaystyle\oint_{C}({y^2+x^2})\,\mathrm{d}s$$
I can see that $x^2+y^2=25$ so $r^2=25 \to r=5$
then:
$$\int_0^{2\pi}\int_0^5r^2r\,drd\theta=\frac{625\pi}{2}$$ which is wrong answer. I know that there is somewhere some stupid mistake but I can't see it.
Hint: $$\displaystyle\oint_{C}({y^2+x^2})\,\mathrm{d}s=5^2\oint_{C}\mathrm{d}s=5^2\cdot2\pi\cdot 5.$$