Line Integrals of Vector Fields

Practice Questions

Calculus 3 › Line Integrals of Vector Fields

Questions

Find the work done by a particle moving in a force field , moving from to on the path given by .

Evaluate the integral $\int \vec{F}\cdot d\vec{r}$ on the curve $\vec{r}(t)=\left \langle t^3, t^2, t+2\right \rangle$ , where $\vec{F}=\left \langle xz, yz, xy\right \rangle$ , on the interval $0 \leq t \leq 1$

Evaluate $\int \vec{F}\cdot d\vec{r}$ on the curve $\vec{r}(t)=\left \langle 2t, 3t, t^3\right \rangle$ , $0\leq t \leq 1$ , where $\vec{F}=\left \langle 2xz, y^2, z^2\right \rangle$ .

Calculate $\int \vec{F}\cdot d\vec{r}$ on the interval $0\leq t \leq1$ , where $\vec{F}=\left \langle x, xy, z^2\right \rangle$ and $\vec{r}(t)=\left \langle 2t^2, t+2, t\right \rangle$

Evaluate $\int_C \vec{F}\cdot d\vec{r}$ , where $\vec{F}(x,y,z)=10x^2y^2z^3\vec{i}+5z\vec{j}+2yz\vec{k}$ , and is the curve given by $\vec{r}(t)=t\vec{i}+t^2\vec{j}+t^3\vec{k}$ , $0\leq t \leq 1$ .

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