If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Evaluating integral for shell method example

Evaluating the definite integral set up using the shell method. Created by Sal Khan.

## Want to join the conversation?

• Wouldn't it have been easier to just put this into the calculator and save 7 minutes?
• I'm assuming he's showing this to demonstrate how to do this sort of problem if you don't have access to a calculator. On an AP Exam, for example.
• The fraction -2835/4 should of been -2835/20. Was bugging me lol
• Yes, he should've since he multiplied -567 by 5.
• Why is there an extra x-value in the problem? I only see the one function, I see no y=x anywhere....
• The extra x comes from the circumference part of the problem. The radius of the shell is x, so 2πr = 2πx. Then we multiply this by the height, which is in terms of x.
• would it have been easier to add the fractions with the same denominator first for example
2pi { (243/5 - 567/4 + 135 - 81/2) - (1/5 - 7/4 + 5 -9/2)} =
2pi (242/5 - 560/4 +130 -72/2) =
2pi (242/5 -140 +130 -36) =
2pi(242/5 -46)=
2pi(242/5 - 230/5)=
2pi * 12/5=
24pi/5
• you know, there are many different ways to do maths, especially arithmetic...
• It would have been much easier to combine the fractions with CD before find a LCD
• I did that and found it much easier. In fact, the combined -560/4 simplifies to -140 and -72/2 simplifies to -36. The only fractional term remaining was 242/5.
• When Sal does the powers of 3. 3^3 3^4 3^5 is he using some trick/method that looks at 3^3 to get 3^4 and looks at 3^4 to get 3^5 or is he just writing them all out from memory?
• I think he just multiplies each answer by three to get the next one. I'd assume that'd be the easiest way to do it.
• What is the difference between the shell method and the washer method?
(1 vote)
• The washer method is based on the volume of an infinitesimally short cylinder with finite circular area, whereas the shell method is based on the volume of an infinitesimally thin cylindrical shell with finite height and radius.

The washer method uses two circles to calculate the infinitesimal volume; the shell method essentially uses a rectangle, just wrapped into a circle with a given radius.

Hope that makes sense; if not, I can try to clarify further.
• why did your 15x^2 turn into (5x^3)/3? isnt it supposed to be (15x^3)/3
(1 vote)
• 15x^2, when integrated, does become (15x^3)/3. Which is why he simplified it to 5x^3. I'm not sure where you got the (5x^3)/3 from.