1. 7.2 Volume: The Disc Method The area under a curve is the summation of an infinite number of rectangles. If we take this rectangle and revolve it about a line, we have a disc.

2. Disc This disc is nothing more than a cylinder on it’s side. The volume of a cylinder is: If we sum up an infinite number of cylinders, we have the new integration formula: This equation is for a horizontal axis of revolution. r r = h & w = dx

3. Vertical axis of revolution

4. Ex. y = x 2, y = 0, and x = 2 about the x-axis r = y

5. Ex. y = x 2, x = 0, and y = 4 about the y-axis r = x

6. Find the radius for y = x 2, y = 0, and x = 2 about the line x = 2 2 x r = 2 - x about the line x = 3 x = 3 4 4