Use la parametización: $C:r(t)=(1,1,0)+t[(1,2,2)-(1,1,0)],t\in [0,1]$

Se omite.

Parametrizamos las curvas,

$C_1:r_1(t)=\text{cos}<!--\; FUNCTION\; APPLICATION\; -->ti+\text{sen}<!--\; FUNCTION\; APPLICATION\; -->tj+0k$ con $t\in [0,\pi ∕2].$

$C_2:r_2(t)=A+t(B-A)=2ti+(t+1)j+3tk,t\in [0,1].$ $$\begin{array}{rcll}{\int \; <!--\; nolimits\; -->}_{C}x\mathit{dx}+z\mathit{dy}+\mathit{dz}& =& {\int \; <!--\; nolimits\; -->}_{C_1}x\mathit{dx}+z\mathit{dy}+\mathit{dz}+{\int \; <!--\; nolimits\; -->}_{C_2}x\mathit{dx}+z\mathit{dy}+\mathit{dz}& \\ & & & \\ & =& {\int \; <!--\; nolimits\; -->}_0^{\pi ∕2}-\text{cos}<!--\; FUNCTION\; APPLICATION\; -->t\text{sen}<!--\; FUNCTION\; APPLICATION\; -->t\mathit{dt}+{\int \; <!--\; nolimits\; -->}_0^{1}4t+3t+3\mathit{dt}& \\ & & & \\ & =& -{\displaystyle \frac{1}{2}}+{\displaystyle \frac{13}{2}}=6.& \end{array}$$