Question

Integral Calulus Question! How to find the volume using "disk", "shell" and "washer"? No drawings needed...just concepts are fine..but drawings will be appreciated :DDD

Answer 1

honestly...i do not understnad textbook definitions =_= they tend to be poetic

Answer 2

this is not a textbook definition

Answer 3

it's not?

Answer 4

seems textbook-y to me

Answer 5

no
its mine own

Answer 6

ugh it's deep @_@ i cannot understand it sorry

Answer 7

@lgbasallote Do Khan academy.

Answer 8

=_=

Answer 9

that was like saying go google it...

Answer 10

Those without the will to learn will not learn 0.o

Answer 11

http://www.khanacademy.org/math/calculus/v/solid-of-revolution--part-1

Answer 12

i have a preference of learning

Answer 13

unffortunately dear old khan does not provide me with that preference

Answer 14

Well, too bad for you. That's all your getting from me.

Answer 15

Why not khan academy, anyways?

Answer 16

1) like i said above i do not like textbook definitions...i get intimidated with deep technical words

2) i do not like videos

3) i do not like listening to stuff..it bores me

4) if i can understand a video i wouldve just listened to my teacher skim through her powerpoint

5) no interaction

6) i have my preferences

7) dear old khan does not satisfy nor provide my preferences

Answer 17

8) i am loyal to openstudy

Answer 18

Fine. Here's the explanation. You are going to have trouble. These are solids of revolution. Very hard to draw. I'm not going to draw them. And, you won't find many people that will.

Answer 19

When you do find someone that will, they will give you an explanation about as good as a textbook or as khan academy

Answer 20

like i said...i just need concept thing...drawings confuse me too

Answer 21

Well, these are solids of revolution. It's not like there's an easier way to explain them than to draw them 0.o

Answer 22

Disk method breaks up the solid into disks of width dx. Shell method I forget

Answer 23

just the formulas will be fine

Answer 24

omg. If you wanted the formulas, you could've just looked at a textbook -_-

Answer 25

the formulas in my book are confusing -_-

Answer 26

State the formulas in your book and I'll see what I can do 0.o

Answer 27

now that i look at it...i dont even know which of these is the formula @_@ seriously...this book does not make sense to me -__- i hate these mathematicians who use hifalutin words and figures :/

Answer 28

Ok. I'm going to look at my book. And give you those formulas.

Answer 29

that'll help

Answer 30

The volume of the entire solid of revolution from x=a to x=b is
\(\huge \int_{a}^{b}2\pi f(x)dx\)

Answer 31

Chad, are you going to help out, or just mess around?

Answer 32

If you're going to mess around, I suggest you get out, because I'm trying to teach @lgbasallote how to find the volume of a solid of revolution.

Answer 33

this is a general formula?

Answer 34

For disks, yes.

Answer 35

You know how definite integration to find the area under a curve works right? we just cut up the function into a bunch of very thin dx's with a height f(x)

Answer 36

oh wait..this is familiar...this is also expressed as \(\large \int_b^a 2\pi r dx\) right?

Answer 37

Yes, but f(x)=r...

Answer 38

i see i see...and when is the disk used?

Answer 39

"You know how definite integration to find the area under a curve works right? we just cut up the function into a bunch of very thin dx's with a height f(x)
For a solid of revolution, we cut it up lengthwise into a bunch of disks with length dx

Answer 40

Volume by Revolution.
\[V= \pi \int\limits_{a}^{b}y^2dx\]

Answer 41

rohangrr...please get out of chad's account -___-

Answer 42

you knew this...all along @Mimi_x3 =_=

Answer 43

Seriously, if he makes one more post, I'm just going to report him, because he's seriously interfereing with my explanation by spamming.

Answer 44

What's wrong igbiw?

Answer 45

@lgbasallote , are you reading what I posted?

Answer 46

yeah

Answer 47

We cut it up into disks with width dx, and thus radius f(x).

Answer 48

so when is the disk used? i suppose they are not optional...they are only used in certain cases

Answer 49

No, what katty said at
answers.yahoo.com/question/index?qid=20091011233031AArWypV
is correct.

Answer 50

@lgbasallote , sorry, I messed up. Was at the wrong page of my book.

Answer 51

YOU ARE MAKING THE THREAD LAGGY BY POSTNG IRRELEVANT REPLIES >.<

@inkyvoyd so what's right?

Answer 52

Anyways, that handy formula I gave you was the volume for shells and washers.

Answer 53

Disks, is actually this. Give me a second.

Answer 54

Instead of posting 3 4 sentence posts, I'm going to post one 12 sentence post, because I'm sick of being interrupted by chad.

Answer 55

oh my..i was wondering why there wasnt an h...i could remember an h with 2 pi r haha

@CHAD159753 i am asking for formulas NOT examples

Answer 56

so \(V = \pi \int_a^b r^2 dx?\)

Answer 57

Yes, @lgbasallote

Answer 58

since it's dx i assume it revolves horizontally...

Answer 59

Now, thought of intuitively, we basically just sum up all the cylinders from a to b with width dx, and radius f(x)

Answer 60

\(\huge V=\pi \int_{a}^{b}f(x)^2dx\)

Answer 61

For these you have to sketch it to see where it evolved and where to \(V=V_1-V_2\)
You have to be able to imagine it in 3D..

Answer 62

I simply made the font bigger, and replaced r with f(x), because r is sort of annoying.

Answer 63

We sum up the disks from a to b
These disks have a radius of f(x), and a width of dx.
I've said that like 3 times; let me make a drawing,