On the left you have a system of two equations with the integral value noted and on the right you have a graph of the difference of the two functions with the integral value noted to start with the ability to also show the area.
Use A and B to change the limits of integration for system of equations. Use the slider c to shift the system of equations up and down. Feel free to change the equations using the f(x) and g(x) input boxes. After playing for awhile answer the questions below.

Questions

What do the zeros of the function on the right mean in relation to the system of equations on the left?
When does the area and integral value of the function on right not agree? Which value, if any agrees with the integral of the system of equation?
Make the integral negative by changing the limits of integration.
Make the integral negative by changing f(x) and g(x).