Question

Find the work done by the force field f(x,y,z)=2xi+2yj+4k on a particle that moves along the helix r(t)=2cos(t)i+2sin(t)j+5tk,0≤t≤2π.

Answer 1

`\displaystyle\int_(\mathcal C)\mathbf f\cdot\mathrm d\mathbf r=\int_(t=0)^(t=2\pi)(4\cos t\,\mathbf i+4\sin t\,\mathbf j+20t\,\mathbf k)\cdot(-2\sin t\,\mathbf i+2\cos t\,\mathbf j+5\,\mathbf k)\,\mathrm dt`

`=\displaystyle\int_(t=0)^(t=2\pi)100t\,\mathrm dt=200\pi^2`