Surface of revolution never negative, the area is given by If the curve is described by the function , , then the integral becomes for revolution around the -axis, and for revolution around the "y"-axis (using ). These come from the above formula. For example, the spherical surface with unit radius is generated by the curve , , when ranges over . Its area is therefore For the case of the spherical curve with radius , rotated about the -axis A minimal surface of revolution is the surface of revolution of the curve between two given points which minimizes surface area. A basic
Solid body against. This allows musicians to stop the string in the same place. Ebony, rosewood and maple are commonly used to make the fingerboard. Some electric guitar necks do not have a separate piece of wood for the fingerboard surface. All the solid bodies have variations in scale length or, the length of the strings from the nut to the bridge. The action, or the height of the strings from the fingerboard, is adjustable on solid body instruments. Most solid bodies have controls for volume and tone. Some have an electronic preamplifier with equalization for low, middle, and high frequencies. These