Problem:
Graphically investigate the function
with a = 0 and for various values of x between 0 and 2p.
Visualization:
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:
- Replace the function sin by cos.
- Replace the lower limit, 0, of the integral by other numbers between 0 and 6. Can you explain the change in the graph of the area function?
- Delete the cos and then raise x to various powers. (Highlight x using the mouse and then enter ^2. You may want to zoom in and out and shift the graph.)
This LiveMath notebook was originally written by Earl Fife.