Applet: Area inside sinusoidal curve
The curve $\dlc$ parameterized by $\dllp(t)=(\sin 2t,\sin t)$ for $0 \le t \le \pi$ is the counterclockwise oriented boundary of a region $D$, shown shaded in blue. As you specify $t$ by dragging the green point on the slider, the red point traces out the curve $\dllp(t)$. Alternatively, you can drag the red point around the curve, and the green point on the slider indicates the corresponding value of $t$. One can calculate the area of $D$ using Green's theorem and the vector field $\dlvf(x,y)=(-y,x)/2$.
Applet file: area_inside_sinusoidal_curve.ggb
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