# Line Integrals – A vector function with a parameter t – Exercise 3513

Exercise

Calculate the integral

$$\int_c (x^2+y^2+z^2) dl$$

Where c is

$$r(t)=2\cos t i+2\sin t j +t k$$

And the range of t is

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

$$\int_c (x^2+y^2+z^2) dl=\sqrt{5}(8\pi+\frac{8}{3}{\pi}^3)$$