How do I continue this surface integral?

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I tried to solve this. After find normal vector, I don't know how know how do I continue this.. Question is in this pic. =>]1

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  1. For a problem like this, always start with a sketch. Sketch the direction of the vector field at a few points on the surface.

  2. At some point you will probably want to switch to cylindrical coordinates. You will be able to write $\hat{n}$ as $\hat{r}$ (or $\hat{\rho}$ if you prefer) and the dot product will be easy, too.

  3. Pick a value for $dS$. That will depend on what you have for your integrand (the dot product).

  4. Set up limits of integration. That will depend on your $dS$.