Integral and Area

Areas can only by positive so this illustration shows the integral of a function and the area between the function and the -axis. Different functions can be selected with the drop-down and the limits and can be moved along the axis. The last function on the list can be edited to be any function. Positive integral parts are shown in blue while negative integral parts are shown in a tan color. There is an option to also show the average value of the function over the interval to .
Move the initial integration point so that negative integral parts are formed. How does the integral vary as you move the limits? What happens to the integral and the area if ? For each function move the limits so that the integral is zero.