Just a few more examples -

Ex 5 p. 471 Shell method necessaryFind the volume of the solid formed by revolving the region bounded by the graphs of y = x3 + x + 1, y = 1, x = 1, about the line x = 2.

r = 1

R= 2 - x

3

2 2

0

R r dy 3

2 2

0

(2 ) 1x dy Whoops! Can’t have x inside, yet can’t switch y = x3 + x + 1 to x = y-something

Try disk method:

x

h=y-1

p=2-x

1

0

2 ( ) ( )p x h x dx

Shell method:

1

3

0

2 2 x x x dx 29

15

1

3

0

2 2 ( 1) 1x x x dx

http://youtu.be/CiXME1u-oyU

7.3b p. 472/ 21-29 odd, 31-33. 41, 43

QUIZ 7.3 Thursday, Feb 9