Problem:

Graphically investigate the function

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

Visualization:

Use the following JAVA applet.

Instructions: The blue graph is the graph of the function y = sin(x) between 0 and 2p. The black dot indicates the point (a,0).

Change a:
When the options Choose a or Draw F are chosen, then you can change the value of a by dragging the mouse across the graph or by clicking the left mouse button while the mouse is on the graph.

Change x:
To change the value of x, click the mouse on Choose x and then drag the mouse across the graph or click the left mouse button while the mouse is on the graph. The green dot indicates the point (x,0) and the red dot indicates the point (x, F(x)). F(x), the y-coordinate of the red dot, is the area which is shown in blue. The graph of F between t=a and t=x is drawn in red.

Draw F:
The graph of F between x=0 and x=2p is drawn in red. You can see the effects of changing a on the graph of F by dragging the mouse across the graph or by clicking the left mouse button while the mouse is on the graph.