1. By: Meghan Grubb
Shells Method

2. Shells
With this method, you draw a line segment parallel to the axis of rotation
Forms a cylinder
Surface Area = 2∏rh
Volume =
X is radius
[f(x)-g(x)] is height

3. Example First step – graph the lines given
Second step – find points of intersection
Third step – about y-axis, draw line parallel to y – axis
If about x-axis, draw line parallel to x-axis
Fourth step – put 2∏ in front of integral
Fifth step – plug in boundary limits
dx – use x intercepts, dy – use y intercepts
Sixth step – multiply Radius and Height
Seventh step – plug dx or dy

4. Radius

5. Height Dx problem – top line minus bottom line
Dy problem – right line minus left line

6. Example

7. Example

8. Example First step – graph the lines given
Second step – find points of intersection
Third step – dx? Or dy? Draw line parallel to y = -3
Dy because line is parallel to y-axis
Fourth step – put 2∏ in front of integral
Fifth step – plug in boundary limits
dx – use x intercepts, dy – use y intercepts
Sixth step – multiply Radius and Height
Seventh step – plug dx or dy

9. Example