jsun2015 said:The answer involves x^.5+3 instead of x^.5 -3. I don't understand why you would add instead of subtract 3; y decreased from 0 to -3 when revolved around y=-3
The washer method is a technique used in calculus to find the volume of a solid of revolution by slicing the solid into thin discs or washers and integrating the cross-sectional area of each disc.
The washer method is typically used when finding the volume of a solid that is formed by rotating a bounded area around a specific axis. It is commonly used in problems involving cylinders, cones, and spheres.
To set up the integral for the washer method, you first need to determine the limits of integration, which are typically the bounds of the area being rotated. Then, you need to find the radius and height of each washer and set up the integral using the formula V = ∫abπ(Router)2-π(Rinner)2 dx or dy, depending on the axis of rotation.
The main difference between the washer method and the disk method is that the washer method can be used for solids of revolution with a hole or empty space in the middle, while the disk method can only be used for solids of revolution with no empty space.
Yes, the washer method can be used for non-circular shapes as long as the cross-sectional area can be represented by a function that can be integrated. For example, it can be used for finding the volume of a wine bottle, which has a curved shape that is not circular.