Verifying approach for solving Line integral of kind 1 ( Homework )

Question

I am trying to solve a Line integral of 1nd kind given as follows : $$\int_C(x^2+y^2-2z)dl$$ on the curved line given as follows:$$C:x=4\cos(2t),y=4 \sin(2t),z=6t,t\in[0,3\pi].$$ So i am just using this formula : $$\int_L f(x,y,z)dl= \int_{t_1}^{t_2}f(\varphi(t), \psi(t), \mathcal X(t)) \sqrt{(\varphi^\prime)^2t \ + \ (\psi^\prime)^2t \ + \ \mathcal (X^\prime)^2}dt$$ and I am getting $$\int_0^{3\pi}[16(\cos^2(2t)+\sin^2(2t)\sqrt{64(\cos^2(2t)+\sin^2(2t)+36})]dt \\ \int_0^{3\pi}(160-120t)dt \\ 160t-60t^2 \bigg |_0^{3\pi}=480\pi-540\pi^2$$ unfortunately I don't have the problem's answer so I will be very thankful if someone's see if my approach to the problem is correct.