7.2 Disk and Washer and 7.3 Shell

Question 1

disk method and washer method and shell method equation of area to integrate

Answer 1

disk
pi R^2x

washer
piR^x - pir^2x

shell
2pi rx hx dx

Question 2

equation for volume

Answer 2

V = integral from a to b of area

Question 3

simple steps for volume

Answer 3

1. draw simple graph
2. find intersection points
3. figure out what method to use
   - based on the easier slice being parallel or perpendicular to axis
4. find the stuff you need from the graph
5. put into an integral and solve

Question 4

when to use disk vs washer vs shell - what method to use

Answer 4

1. slice the way it looks easier, less changes from bounds
2. are the slices perpendicular or parallel to the axis of rotation
   - parallel to axis - shell
   -perpendicular to axis of rotation - disk (goes all the way to the axis) and washer (there is a hole)

Question 5

what is hx and rx in the shell method

Answer 5

h - height of the slice
r- radius from slice to the axis of rotation

Question 6

what is R and r in disk and washer method

Answer 6

R = from the far graph to axis
r = from closer graph to axis

Question 7

what do you integrate with respect to in volume questions and area questions

Answer 7

what is changing
how the slice is changing