How to find volume by Washer's Method

1. Volume by Washer Method
MUHAMMAD AHMAD (L1F20BSPH0040)

2. Intro
 We will start looking at the volume of a solid of revolution. We
should first define just what a solid of revolution is. To get a solid of
revolution we start out with a function, y=f(x), on an interval [a , b],
as shown in the figure below:

3.  Suppose the generating region R is bounded by two
functions, y = f(x) on the top and y = g(x) on the bottom, by
revolving the previous figure around X-axis.
 This time, when you revolve R around X-axis, the slices
perpendicular to that axis will look like washer, as shown in the
figure below:

4.  In the figure, y = f(x) is the outer radius of the and y = g(X)
is the inner radius of the washer. Where:
y = f(x) > y = g(x)
Where,
r2 = outer radius of washer
r1 = inner radius of washer
As we know that, typical method to find volume = π r2 h

5.  We’ll need to know the volume formula for a single washer.
V = π (r2
2 – r1
2) h
= π [ f(x)2 – g(x)2 ]
the exact volume formula arises from taking the limit as the number of slices
become infinite.
Washer method : V = π 𝑎
𝑏
[f(x)2 – g(x)2)] dx.
Where a and b is the limit from which area of washer is to be found.