Parameterize the following line integral

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$$\int _{\gamma }xydx\:+zdy\:-yzdz\:$$ where$$\:\gamma \::\:x^2+y^2=4\: \text{and}\:z=x^2+y^2$$

I assumed $$x\left(t\right)=2\cos t\:,\:y\left(t\right)=2\sin t,\:z\left(t\right)=4$$

Is it correct?