1.
Let's practice a second example: Find the work done by the field \(\vec{F}=x\hat{i}+y\hat{j}+z\hat{k}\) along the curve parametrized by \(\vec{r}(t)=\cos(\pi t)\hat{i}+t^2\hat{j}+\sin(\pi t)\hat{k},\ 0\leq t\leq 1\text{.}\)
Answer.\(1/2\)
Section 2.4 Example: Line Integral of a Vector Field
This video gives a concrete example of a line integral along a vector field by choosing a specific parameterization of the curve and computing it all.
Learning Objectives:
- Compute the line integral of a vector field
