 So, let's talk a little bit more physics. Work is the product of force and distance. One special and important type of force is gravitational force. This is so special and important it has a special name. The force of gravity on an object is called its weight. And since the force, it's measured in newtons. Now, remember work is equal to the product of a force and the distance over which the force is applied. And if force or distance is variable, we must use calculus. And this leads to a useful strategy. Take a little bit and a sum to find the total. For example, suppose you're digging a well. The well has the shape of a cylinder 10 meters deep and 1 meter in diameter. The material removed has a weight of 15,000 newtons per cubic meter. So let's determine the amount of work required to dig the well. So again, the useful idea to keep in mind is we want to sum up the slices. Now, the important idea to understand here is that while the weight is a constant, the distance changes. So suppose we've dug x meters down. If we want to remove a disc of dirt dx meters thick, this material has to be moved x meters to the top of the well. So we can remove it. And the force required is the weight. And the thing to recognize here is that the force doesn't actually change. It's always going to be based on this 15,000 newtons per cubic meter. What does change is the amount of distance we have to apply that force. The further down we dig, the further we have to move the dirt. So we note that we're given the quantity in newtons per cubic meter. That's the weight per cubic meter, which means we need to know the volume of the dirt removed. So if we take that thin slice, the volume of a disc of dirt with diameter one meter and dx meters thick, well, that's the volume of a very short cylinder pi r squared h. Since the diameter of the cylinder is one meter, that means the radius is one half meter. And since we're taking a slice, the thickness is going to be a little bit of x dx. And that gives us our volume. So the weight will be the volume times the density 15,000. So remember, work is a product of force and distance. So that little slab has a weight of 3750 pi dx newtons. Now we have to bring it up to the top of the well. And that's going to require us to move at a distance of x meters. And so the work done will be the product of the weight, 3750 pi dx, times the distance we have to move that weight, x meters. Now that's just the work for removing that one slab of dirt. We'll need to sum up the work done for removing all those slabs. Now, since our well is 10 meters deep, those x values are going to go from 0 meters, that's the top, down to 10 meters, that's the bottom of the well. And at this point, the hard part is done. All we have to do is evaluate a definite integral and we find...