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:

- 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.