line integral, then mass of the line

Question

I have a line is lying along the curve parameterized at $x = 5cos (t), y = 5sin (t), z = 2t$ for $0≤t≤\pi$.

What is the mass of the wire if its mass density is given by$ ρ (x, y, z) = z?$

I have tried this for a long time, cant seem to figure out the correct answer, im sure its simple tho.

How do i calculate the mass of this wire, and how do i calculate it the correct way?

Answer 1

HINT

• consider the parametrization $((x(t),y(t),z(t))\quad t\in [0,\pi]$
• set up and calculate the line integral $\int_L \rho ds=\int_{0}^{\pi} z(t)\sqrt{x'(t)^2+y'(t)^2+z'(t)^2}dt$