Line integral on cylindrical coordinates.

Question

Question

Hello, i am having problem with line integral in cylindrical coordinates and especially with this question. I can do the radial lines, but the line integral of 2 straight lines are just coming out wrong and it doesn't match with the Stoke's theorem either. Are there any mistakes with my work?

My Work

Answer 1

Note that along line $\vec l$ we have for $t\in[2,5]$

• $\vec l(t)=(7-t) \vec a_{\rho}+\frac{\pi}3\vec a_{\phi}\implies \frac{d\vec l}{dt}=-\vec a_{\rho}$