The Area Function


The left applet shows `int_a^x f(t) dt` represented as an area. Carefully notice how the variables `a`, `x`, and `t` relate to each other -- we are using a `t`-axis, not an `x`-axis! By selecting "Show Trace" on the right applet, you can see the area graphed as `x` (or `a`) changes. Notice that the right applet has an `x`-axis. To clear the drawing on the right, unselect the check box.


  1. Put `a = 1` and move `x` slowly to see what graph emerges on the right. How does the `x`-value on the left applet relate to the `x`-value on the right applet?
  2. Put `a = 0` and repeat the above process. How does this new graph compare to the one you made before?