# Line Integrals – 3 variable vector function – Exercise 3516

Exercise

Calculate the integral

$$\int_c (2z-\sqrt{x^2+y^2}) dl$$

Where c is

$$r(t)=t\cos t i+t\sin t j +t k$$

and the range of t is

$$0\leq t\leq 2\pi$$

$$\int_c (2z-\sqrt{x^2+y^2}) dl=\frac{\sqrt{8}}{3}[\sqrt{{(1+2{\pi}^2)}^3}-1]$$