Finding Volumes Of A Solid

Question 1

When is disk method used?

Answer 1

When the defined region border the axis of revolution over the entire interval (a, b)

Question 2

Disk method revolving around x-axis

Answer 2

Volume = π ∫ [ f(x) ]² dx

Question 3

Disk Method revolving around y-axis

Answer 3

Volume = π ∫ [ f(y) ]² dy

Question 4

Disk Method revolving around horizontal line y = k

Answer 4

Volume = π ∫ [ f(x) - k ]² dx

Question 5

Disk Method revolving around vertical line x = m

Answer 5

Volume = π ∫ [ f(y) - m ]² dy

Question 6

How do we get volume if given Area f(x)

Answer 6

∫ f(x) dx
Integrate area from a to b

Question 7

When is Washer Method used?

Answer 7

When the defined region has a space between the axis of revolution on the interval (a, b)

Question 9

How many functions make up the Washer Method?

Answer 9

2 functions

Question 10

When using washer method which should be first?

Answer 10

f(x)
The top function

Question 11

Washer Method revolving my around the x-axis

Answer 11

π ∫ [ f(x) ]² - [ g(x) ]² dx