Volume by WASHER METHOD


(Region revolved about the x-axis)
2
2
V     outer radius    inner radius  dx

a 
EXERCISES:
b


    f  x     g  x  dx
a
b
2
2

1.
2.
3.
4.
5.
6.

(Region revolved about the y-axis)
2
2
V     outer radius    inner radius  dy

c 
d

d
c
  f  y 
2

  g  y  dy
2
Find the volume of the solid obtained by revolving the region
bounded by y  x and y  x
1. about the x-axis.
2. about the y-axis.
7. y  x 2 , y  2  x 2 ; about the x-axis
8. x 2  y 2  1, y 2 
3
x, y  0; about the x-axis  the smaller region 
2
9. x 2  y 2  1, y 2 
3
x, y  0; about the y -axis  the smaller region 
2
3. about the line y  2
3
1
10. y  ln x, y  x  , y  0, y  , x  2; about the y -axis
2
2
