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Area of a surface of revolution question

I need to find the arc of the asteroid x=acos3t;y=asin3t x=acos^3t ; y=asin^3t that lies above the x axis.

My workings so far are:
image.jpg

I missed a few stages out.. But I'm pretty sure my workings are correct.. I hope.. I'm just wondering what my limits would be? I though 0 and pi, but that would reduce the value of my integral to 0.. Help anybody? :biggrin:
(edited 10 years ago)
image.jpg234.2KB
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Reply 2
Avatar for Phichi
Phichi
11
Are you referring to arc length? If so, you shouldn't have 2pi at the front of your integral, nor y. Integrate from 0 to pi, indeed :smile:

Here's what I mean by your stray y and 2pi.

(Too lazy to latex it)

(edited 10 years ago)
Original post by CharlieBoardman
I need to find the arc of the asteroid x=acos3t;y=asin3t x=acos^3t ; y=asin^3t that lies above the x axis.

My workings so far are:
image.jpg

I missed a few stages out.. But I'm pretty sure my workings are correct.. I hope.. I'm just wondering what my limits would be? I though 0 and pi, but that would reduce the value of my integral to 0.. Help anybody? :biggrin:


y >0 for sint>0 so limits are -pi/2 to pi/2.
Incidentally, are you finding arc length or area?
(edited 10 years ago)
Original post by brianeverit
y >0 for sint>0 so limits are -pi/2 to pi/2.
Incidentally, are you finding arc length or area?


if y>0 for sint>0 then surely you want from 0 to pi?
Original post by newblood
if y>0 for sint>0 then surely you want from 0 to pi?


That's what I thought too.

Spoiler

(edited 9 years ago)
Original post by Kotoamatsukami
That's what I thought too.

Spoiler



yes i got 6a for the whole curve, so above axis is half that 1st quadrant is replicated in all others by symmetry

well done rahul
Original post by newblood
yes i got 6a for the whole curve, so above axis is half that 1st quadrant is replicated in all others by symmetry

well done rahul


Nice! I used a different method to evaluate the integral directly. It involved modulus curves.

Spoiler

(edited 9 years ago)
Original post by Kotoamatsukami
Nice! I used a different method to evaluate the integral directly. It involved modulus curves.

This isn't Rahul but it's somebody else you know from TSR, who also happens to know Rahul :tongue:


cartesian equation is x^2/3+y^2/3=a, so that would be quite easy to integrate. i just got 3a/2 for 1st quadrant then multiply by 2 or 4 for whatever region you want

What makes you think i know you, just cuz i know rahul

I kno rahul, but he doesnt know me :colone:
Original post by newblood
cartesian equation is x^2/3+y^2/3=a, so that would be quite easy to integrate. i just got 3a/2 for 1st quadrant then multiply by 2 or 4 for whatever region you want

What makes you think i know you, just cuz i know rahul

I kno rahul, but he doesnt know me :colone:


I decided to use the arc length integration formula and ended up with

ℓ=3a2∫0π∣sin⁡2t∣ dt\displaystyle \ell = \dfrac{3a}{2} \int_{0}^{\pi} \left| \sin 2t \right| \text{ d}t

Spoiler

(edited 9 years ago)
Original post by Kotoamatsukami
I decided to use the arc length integration formula and ended up with

ℓ=3a2∫0π∣sin⁡2t∣ dt\displaystyle \ell = \dfrac{3a}{2} \int_{0}^{\pi} \left| \sin 2t \right| \text{ d}t

Spoiler



but rahul is an omniscient juju man :colone:
Original post by Kotoamatsukami
I decided to use the arc length integration formula and ended up with

ℓ=3a2∫0π∣sin⁡2t∣ dt\displaystyle \ell = \dfrac{3a}{2} \int_{0}^{\pi} \left| \sin 2t \right| \text{ d}t

Spoiler



Uchiha Shisui we still on for playing football today :colone:

newblood quote me, par me, rep me, praise me, but only when you have the same mathematical ability come before me, until then revise and cling to your SS dream (no cambridge offer) :biggrin: he lacks pain and hatred by enourmous amounts :wink:
Original post by Rahul.S
Uchiha Shisui we still on for playing football today :colone:

newblood quote me, par me, rep me, praise me, but only when you have the same mathematical ability come before me, until then revise and cling to your SS dream (no cambridge offer) :biggrin: he lacks pain and hatred by enourmous amounts :wink:


Of course!

That Itachi quote :coma:
Original post by Rahul.S
Uchiha Shisui we still on for playing football today :colone:

newblood quote me, par me, rep me, praise me, but only when you have the same mathematical ability come before me, until then revise and cling to your SS dream (no cambridge offer) :biggrin: he lacks pain and hatred by enourmous amounts :wink:


Prettyhard to get an offer when you have not yet applied :wink:

You yourself told me i would undoubtedly get SSS in step

But until then i shaallrevise S2,
Original post by newblood
Prettyhard to get an offer when you have not yet applied :wink:

You yourself told me i would undoubtedly get SSS in step

But until then i shaallrevise S2,


you have potential young one, to become a vessel worth testing my strength and abilities with, grow hatred and cause pain, only when you get a S in STEP can you try sending for me-otherwise you can bring your whole crew and it will be GAMEOVER

https://www.youtube.com/watch?v=vst68fWWtXk

off to park with Uchiha Shisui come along init?
Original post by Rahul.S
you have potential young one, to become a vessel worth testing my strength and abilities with, grow hatred and cause pain, only when you get a S in STEP can you try sending for me-otherwise you can bring your whole crew and it will be GAMEOVER

https://www.youtube.com/watch?v=vst68fWWtXk

off to park with Uchiha Shisui come along init?



dont @ me with ghetts, all i gotta do is bring p money and your done for
Original post by newblood
dont @ me with ghetts, all i gotta do is bring p money and your done for


that shows how much you know of the grime scene and grime as a whole :redface: Focus on step :colone:
Original post by Rahul.S
that shows how much you know of the grime scene and grime as a whole :redface: Focus on step :colone:


idc how much i know about grime or grime as a whole. i jus listn to it, i dont bum it lmao

but wise words, as off tomoro i shall focus on step. eyes on the prize g
Original post by newblood
idc how much i know about grime or grime as a whole. i jus listn to it, i dont bum it lmao

but wise words, as off tomoro i shall focus on step. eyes on the prize g


ive been recording and clashing since i was a kid, hitting dj limelight's studio and still yet to lose a clash, p money no doubt overall won the dub war but ghetts last eiffel tower was soo good that most people are split in regards to who won? That tested their abilities in war dubs and a proper clash is the ONLY way to sort it out, ghetts backed out of that because what is it going to get him? Those days I rated p as the best grime mc, now his a myth and ghetts is still doing his thing as j.clarke. Check some old stuff ghetts did, he gets people hyped like no one else, well maybe maxsta when he sent for chippy but last week I clocked that guy working in my local chippy :colone:

GL WITH STEP :colone: COME DOWN BARKING PARK ONE DAY, PLAY BALL INIT

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