Area Between Curves
The goal of this applet is not to calculate the area between two curves but to look at different cases. The students are encouraged to change the graphs and see how the integration intervals change.
Given are two functions f(x)=c(x-x1)(x-x2)(x-x3)(x-x4) and g(x)=0.6x+constant. We want to find the area surrounded by the two curves y=f(x) and y=g(x) and the vertical lines through a and b. You can study this problem by experimenting with different graphs. The area for each interval and the total area are calculated in the spreadsheet. The value of the definite integral of the difference f(x)-g(x) from a to b is given in cell B10 for comparison with the area between the curves.
Drag the slider "Select Interval" to see the area in each interval. If f(x)>g(x), the area is colored in red; If f(x)