Graphically investigate the function

with a = 0 and for various values of x between 0 and 2p.

The following LiveMath notebook is an animation of such an investigation.

The animation shows the area bounded by the thick black line which is the graph of y = sin(t), the t-axis, and the blue line t=x for various increasing values of x. The thick red line is the graph of y = F(x), the area function.

Additional Examples:

This LiveMath notebook was originally written by Earl Fife.