What is the area bound by two intersecting functions?

[Sky.Anthony]

Homework Statement

I am given the following two functions: y=x³-13x²+40x and y=-x³+13x²-40x

I need to find the area bound between the above two functions.

Homework Equations

Integrals!

The Attempt at a Solution

I don't know how to do this as there is 3 points of intersection at x= 0,5,8. I know that I have to do the sum of two integrals, but I don't know what functions are supposed to go under each integral. One of the integrals will obviously have an upper limit of 5 and lower limit of 0 and the other one has upper limit of 8 and lower limit of 5 but as for the functions that go with these integrals, I have no idea. In addition, can someone explain to me how I can tell which functions will be the one on "top" (ie, for areas and volumes, you subtract the "lower" function from the "upper" function but how can I tell which one is bigger?)?

 

[Dustinsfl]

You need to see if the area between the functions is horizontal or vertically simple. Some times you may have to do 2 or 3 separate integrals due to one section being vertical and the next horizontal. The top function minus the bottom function or you can take a double integral.

 

[Dustinsfl]

Looking at the graphs, we see that the first equation is above the 2nd until the 2nd point of intersection. You can subtract top from the bottom and integrate. Then do the same for the 2nd piece. You may come back with zero as the answer. If so, integrate the the first equation to the 2nd point on intersection and multiple by 2. By ignoring the bottom piece, you have to multiply by 2.

 

[Sky.Anthony]

Nevermind. I figured it out :D The answer is 863/3... just fyi.