[tex]\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[/tex]
[tex]=\displaystyle\int_{t=0}^{t=2\pi}100t\,\mathrm dt=200\pi^2[/tex]
