Evaluate the line integral ∫CF⋅dr\int_C \mathbf{F} \cdot d\mathbf{r}∫CF⋅dr for F(x,y,z)=⟨2x,2y,2z⟩\mathbf{F}(x, y, z) = \langle 2x, 2y, 2z \rangleF(x,y,z)=⟨2x,2y,2z⟩ along the helix r(t)=⟨cost,sint,t⟩\mathbf{r}(t) = \langle \cos t, \sin t, t \rangler(t)=⟨cost,sint,t⟩ for 0≤t≤2π0 \le t \le 2\pi0≤t≤2π.
4π24\pi^24π2
000
2π2\pi2π
111