Some pictures illustrating line integrals and work

Simple example from the text

An illustration of $$\int_C {\bf F} \cdot d{\bf r},$$ where ${\bf r}(t) = \langle t,t^2 \rangle$ and ${\bf F} (x,y) = \langle x\sin(y),y \rangle$.

A harder example

An illustration of $$\int_C {\bf F} \cdot d{\bf r},$$ where $ {\bf r}(t) = \left\langle \left(4\pi/3-t\right)\cos\left(2 \left(4\pi/3-t\right)\right), \left(4\pi/3-t\right)\sin\left(2\left(4\pi/3-t\right)\right) \right\rangle $ and $${\bf F} (x,y) = -\frac{\langle x,y \rangle}{(x^2+y^2)^{3/2}}.$$