# Homework Help: Area of a tunnel with two functions creating the cross section

1. Apr 13, 2013

### Creaturemagic

1. The problem statement, all variables and given/known data
Two curves/functions make up one side of a tunnel (the tunnel is symmetrical, so the other side is the same)
Function 1: y = 5 + (2/((x-4)^3))
Function 2: y = (x -1)^3 - 5
I need to find the area of the tunnel, so I can find the amount of dirt that needs to be removed,
So I need the area of one side of the tunnel cross section.

This is what it looks like with both functions. Where they meet at X = 3 and Y = 3, is where they join.
http://img203.imageshack.us/img203/9497/04142013image003.jpg [Broken]

So The top of the tunnel is Function 1, when F1 meets Function 2, function 2 becomes the side of the tunnel. The tunnel cross section looks like this:
http://img703.imageshack.us/img703/8360/tunnela.png [Broken]
Remembering this is just the right side of the tunnel, the left side is the same, flipped over the Y axis, to form a full tunnel.

2. Relevant equations

I thought it would just be an integral with limits, but the more I thought about it, the less I believed that was correct. I don't really know what equation to use to find the area when the curves only intercept once not twice.