At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions.

See more answers at brainly.com

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions

HA!! shells, i knew they were comin

since we is going around the y axis; its simpler right now

yup :( i never used this method before ><

the radius of each shell moves from x=0 to x=1 right?

yup

and the height of each shell is determined by: f(x)

wait, i know why its x=1, but why is it x=0

so the area of each shell, when flattened out is height* width...

umm... y axis means x=0 they are the same thing

ohh okay gotcha

2pi [S] x(x^2) dx ; [0,1]
2pi x^4
------- = (pi x^4)/4 = pi/4
4

how did you get rid of the 4th power in the numerator?

you dont... why would you?

but you put (pi x^4)/4 = pi/4
where did the 4th power go?

F(0) = 0
F(1) = pi/4
F(1) - F(0) = pi/4

over 2 lol

i forgot i changed 2/4 to 1/2.... doh!

\[\frac{2\pi x^4}{4} = \frac{\pi x^4}{2}\]

much clearer, lol thank you :D

when im wrong; say im wrong...not ask me how im right lol. I just assume im right ;)

lol will do xD

you understand the mechanics of the shell method tho?

correct

the width = 2pi x...can you tell me why?

we aint using half the shell, but the whole thing

i think it has to do with the radius, is that why the width is 2 pi x?

ohh is it the circumference of the cylnder?

it does, but i want to make sure you understand this :) its very basic and easy...exactly lol

lol i took a careful look at the cylinder and realized haha xD

you did good :)

the shell method makes things easier for some problems

{S} 2pi x[f(x)] dx is what we do right?

if there is a constant we can pull it aside right?

mhmm

the 2pi

2 pi goes out and what are we left with inside?

x*f(x)

excatly; so we integrate 'x*f(x)'

do you se how that differes from your first statement of ; we int f(x)?

yesss, thanks for clearing that up for me :) this method seems a bit easier than the others lol

the disc method take all the areas of a given circle; with a radius of f(x) and adds them up

volume is always a positive number

what is the formula for the the area of a circle ?

and area of circle is pi r^2

so f(x) is the radius?

and tell me what the radius of each given circle is?

oh, f(x) xD haha

that is all these volume of rotation problems amopunt to :)

lets say 4 high and 4 wide; the area should be 16 right?

correct

if we integrate f(x) = y = 4; from -2 to 2 we know we should get 16 right?

how come its from -2 and 2?

the distance from -2 to 2 = 4 right?

yupp

and a square with sides = 4 would straddle the y axis would sit from -2 to 2 on the x axis right?

correct. i gotcha now :) lol

it really is. thank you for that :D

once we can draw a picture, the rest is just intuitive

youre welcome :)