Ampère's law for two circular loops: doubts for an image of my italian physics textbook

Starting from this image, I have two loops $$S_1$$ and $$S_2$$ with two batteries where the currents $$I_1$$ and $$I_2$$ flows with clockwise verse. The line $$\Gamma=\ell$$ have always a clockwise verse.

My solution with Ampère's law is $$\oint_{\Gamma} \vec{B}\cdot d\vec{\ell}=\mu_0I_{\text{enc}}$$ where the total current concatenated $$I_{\text{enc}}$$ with the path is equal to $$I_{\text{enc}}=-I_1+2I_2$$. If I'm following the right hand rule, shouldn't the grey arrows of the curve be placed in the anti-clockwise direction?

I am not very convinced of the correctness of this image, and I hope to have welcome answers. Thank you very much.

• The symbol $I$ in there... is it what you call $\ell$ or is it a current $I$? May 4, 2020 at 21:29
• @ZeroTheHero It is \Gamma=\ell. May 4, 2020 at 21:30

You are right. The line integral in the direction shown in the diagram comes to $$\mu_0 (I_1-2I_2)$$. Alternatively we could reverse the arrows on the grey path, in which case the line integral would come to $$\mu_0 (2I_2-I_1)$$.