The washer method is a technique used to find the volume of a solid of revolution when the solid has a hole in the middle. It involves integrating the difference between the outer radius and inner radius squared, multiplied by $\pi$.
congrats on reading the definition of washer method. now let's actually learn it.
The washer method is typically used when the solid of revolution is generated by rotating a region around an axis that results in a hollow object.
The formula for volume using the washer method is $$V = \pi \int_{a}^{b} [(R(x))^2 - (r(x))^2] dx$$, where $R(x)$ and $r(x)$ are the outer and inner radii, respectively.
Ensure that $R(x)$ and $r(x)$ are correctly identified based on the axis of rotation and positions of functions involved.
The limits of integration $[a,b]$ should match the region being revolved around the axis.
A common mistake is forgetting to square both radii before subtracting and integrating.
Review Questions
What is the key difference between the disk method and the washer method?
How do you determine which function represents $R(x)$ and which represents $r(x)$?
Write down and explain each part of the formula for calculating volume using the washer method.