$M \subset \mathbb{R}^3$ is a rotation of set $\{ x^2 + z^2 = 4x-3, 1

$M \subset \mathbb{R}^3$ is a surface created by rotation of set$\{ x^2 + z^2 = 4x-3, \ 1<x<2, \ -1<z<1 \}$ by $\pi$ around axis OZ.

Find $\int_M \max(x,y,z) d \lambda_2$.

I know that $x^2 + z^2 = 4x-3 \iff x^2 - 4x + 4 + z^2 = 1 \iff (x-2)^2 + z^2 = 1$

So, we have a circle with radius equal to $1$ and with center in $(x = 2, z = 0)$. The values of x and z make it possible for the whole circle to appear. When we rotate it around OZ axis, we will obtain a part torus (not the full torus since we rotate only by $\pi)$. The values of x and y change as we rotate and the values of z stay constant.

As I see that, we have such situation:

But what to do next? How to calculate such an integral?