Find the area between the curves:
y=x^3-12x^2+20x and
y=-x^3+12x^2-20x
first, find where the curves intersect. by setting them equal to each other and solving for x. let's say they intersect for and , where . then these are your limits of integration.
now we need to check which graph is above which. you can simply plug in a value between and and see which function gives the higher value. (it is an extremely good idea to graph the curves. just in case they enclose more than one area. you can use a graphing utility to do this)
Now, let the area between the curves be .
we have
can you continue?