surface area of a parametric curve or revolution

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
0
down vote

favorite












I have the equations $x=9t-3t^3 $ and $ y=9t^2$ , $0le tle 2$ rotated about the x-axis



what I did to try and solve this was:



$ S= int^2_0 2pi(9t^2) sqrt(9-9t^2)^2+(18t)^2dt $



$S= int^2_0 18pi t^2 sqrt81t^4 +162t^2+81dt $



$ S=int^2_0 18pi t^2 (9-9t^2)dt $



$S= int^2_0 162pi t^2 (t^2+1) dt $



$ S= 162pi [fract^55 +fract^33] $



$ S= frac7344pi5$



I'm not sure where I went wrong , any help pointing that out is greatly appreciated.




parametric surface-integrals




share|cite|improve this question



















  • Hence you are claiming you went wrong somewhere I guess you know the right solution. Could you please add the right one somewhere? I think it is easier to seach for a mistake by knowing what the outcome should look like.
    – mrtaurho
    Aug 7 at 21:06










  • Furthermore I have to say that I cannot spot any mistake beside the typo with the third line where it should be $(9+9t^2)$.
    – mrtaurho
    Aug 7 at 21:12










  • Do you understand "How this curve is"?　Your calculation is correct when x increase monotonically.
    – Takahiro Waki
    Aug 7 at 21:28










  • wolfram alpha show this curve need a few integrals. wolframalpha.com/input/?i=x%3D9t-3t%5E3,y%3D9t%5E2,+0%3Ct%3C2
    – Takahiro Waki
    Aug 7 at 21:35















up vote
0
down vote

favorite












I have the equations $x=9t-3t^3 $ and $ y=9t^2$ , $0le tle 2$ rotated about the x-axis



what I did to try and solve this was:



$ S= int^2_0 2pi(9t^2) sqrt(9-9t^2)^2+(18t)^2dt $



$S= int^2_0 18pi t^2 sqrt81t^4 +162t^2+81dt $



$ S=int^2_0 18pi t^2 (9-9t^2)dt $



$S= int^2_0 162pi t^2 (t^2+1) dt $



$ S= 162pi [fract^55 +fract^33] $



$ S= frac7344pi5$



I'm not sure where I went wrong , any help pointing that out is greatly appreciated.




parametric surface-integrals




share|cite|improve this question



















  • Hence you are claiming you went wrong somewhere I guess you know the right solution. Could you please add the right one somewhere? I think it is easier to seach for a mistake by knowing what the outcome should look like.
    – mrtaurho
    Aug 7 at 21:06










  • Furthermore I have to say that I cannot spot any mistake beside the typo with the third line where it should be $(9+9t^2)$.
    – mrtaurho
    Aug 7 at 21:12










  • Do you understand "How this curve is"?　Your calculation is correct when x increase monotonically.
    – Takahiro Waki
    Aug 7 at 21:28










  • wolfram alpha show this curve need a few integrals. wolframalpha.com/input/?i=x%3D9t-3t%5E3,y%3D9t%5E2,+0%3Ct%3C2
    – Takahiro Waki
    Aug 7 at 21:35













up vote
0
down vote

favorite









up vote
0
down vote

favorite











I have the equations $x=9t-3t^3 $ and $ y=9t^2$ , $0le tle 2$ rotated about the x-axis



what I did to try and solve this was:



$ S= int^2_0 2pi(9t^2) sqrt(9-9t^2)^2+(18t)^2dt $



$S= int^2_0 18pi t^2 sqrt81t^4 +162t^2+81dt $



$ S=int^2_0 18pi t^2 (9-9t^2)dt $



$S= int^2_0 162pi t^2 (t^2+1) dt $



$ S= 162pi [fract^55 +fract^33] $



$ S= frac7344pi5$



I'm not sure where I went wrong , any help pointing that out is greatly appreciated.




parametric surface-integrals




share|cite|improve this question











I have the equations $x=9t-3t^3 $ and $ y=9t^2$ , $0le tle 2$ rotated about the x-axis



what I did to try and solve this was:



$ S= int^2_0 2pi(9t^2) sqrt(9-9t^2)^2+(18t)^2dt $



$S= int^2_0 18pi t^2 sqrt81t^4 +162t^2+81dt $



$ S=int^2_0 18pi t^2 (9-9t^2)dt $



$S= int^2_0 162pi t^2 (t^2+1) dt $



$ S= 162pi [fract^55 +fract^33] $



$ S= frac7344pi5$



I'm not sure where I went wrong , any help pointing that out is greatly appreciated.





parametric surface-integrals





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Aug 7 at 20:58









C_bri

112




112











  • Hence you are claiming you went wrong somewhere I guess you know the right solution. Could you please add the right one somewhere? I think it is easier to seach for a mistake by knowing what the outcome should look like.
    – mrtaurho
    Aug 7 at 21:06










  • Furthermore I have to say that I cannot spot any mistake beside the typo with the third line where it should be $(9+9t^2)$.
    – mrtaurho
    Aug 7 at 21:12










  • Do you understand "How this curve is"?　Your calculation is correct when x increase monotonically.
    – Takahiro Waki
    Aug 7 at 21:28










  • wolfram alpha show this curve need a few integrals. wolframalpha.com/input/?i=x%3D9t-3t%5E3,y%3D9t%5E2,+0%3Ct%3C2
    – Takahiro Waki
    Aug 7 at 21:35

















  • Hence you are claiming you went wrong somewhere I guess you know the right solution. Could you please add the right one somewhere? I think it is easier to seach for a mistake by knowing what the outcome should look like.
    – mrtaurho
    Aug 7 at 21:06










  • Furthermore I have to say that I cannot spot any mistake beside the typo with the third line where it should be $(9+9t^2)$.
    – mrtaurho
    Aug 7 at 21:12










  • Do you understand "How this curve is"?　Your calculation is correct when x increase monotonically.
    – Takahiro Waki
    Aug 7 at 21:28










  • wolfram alpha show this curve need a few integrals. wolframalpha.com/input/?i=x%3D9t-3t%5E3,y%3D9t%5E2,+0%3Ct%3C2
    – Takahiro Waki
    Aug 7 at 21:35
















Hence you are claiming you went wrong somewhere I guess you know the right solution. Could you please add the right one somewhere? I think it is easier to seach for a mistake by knowing what the outcome should look like.
– mrtaurho
Aug 7 at 21:06




Hence you are claiming you went wrong somewhere I guess you know the right solution. Could you please add the right one somewhere? I think it is easier to seach for a mistake by knowing what the outcome should look like.
– mrtaurho
Aug 7 at 21:06












Furthermore I have to say that I cannot spot any mistake beside the typo with the third line where it should be $(9+9t^2)$.
– mrtaurho
Aug 7 at 21:12




Furthermore I have to say that I cannot spot any mistake beside the typo with the third line where it should be $(9+9t^2)$.
– mrtaurho
Aug 7 at 21:12












Do you understand "How this curve is"?　Your calculation is correct when x increase monotonically.
– Takahiro Waki
Aug 7 at 21:28




Do you understand "How this curve is"?　Your calculation is correct when x increase monotonically.
– Takahiro Waki
Aug 7 at 21:28












wolfram alpha show this curve need a few integrals. wolframalpha.com/input/?i=x%3D9t-3t%5E3,y%3D9t%5E2,+0%3Ct%3C2
– Takahiro Waki
Aug 7 at 21:35





wolfram alpha show this curve need a few integrals. wolframalpha.com/input/?i=x%3D9t-3t%5E3,y%3D9t%5E2,+0%3Ct%3C2
– Takahiro Waki
Aug 7 at 21:35
















active

oldest

votes











Your Answer




StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);








 

draft saved


draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2875397%2fsurface-area-of-a-parametric-curve-or-revolution%23new-answer', 'question_page');

);

Post as a guest






















active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes










 

draft saved


draft discarded


























 


draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2875397%2fsurface-area-of-a-parametric-curve-or-revolution%23new-answer', 'question_page');

);

Post as a guest
































































-

這個網誌中的熱門文章

How to combine Bézier curves to a surface?

圖片
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite My aim is to smooth the terrain in a video game. Therefore I contrived an algorithm that makes use of Bézier curves of different orders. But this algorithm is defined in a two dimensional space for now. To shift it into the third dimension I need to somehow combine the Bézier curves. Given two curves in each two dimensions, how can I combine them to build a surface? I thought about something like a curve of a curve. Or maybe I could multiply them somehow. How can I combine them to cause the wanted behavior? Is there a common approach? In the image you can see the input, on the left, and the output, on the right, of the algorithm that works in a two dimensional space. For the real application there is a three dimensional input. The algorithm relays only on the adjacent tiles. Given these it will define the control points of the mentioned Bézier cur...
閱讀完整內容

Mutual Information Always Non-negative

圖片
Clash Royale CLAN TAG #URR8PPP up vote 10 down vote favorite 6 What is the simplest proof that mutual information is always non-negative? i.e., $I(X;Y)ge0$ probability-theory share | cite | improve this question edited Jun 17 '12 at 15:38 Cameron Buie 83.6k 7 71 154 asked Jun 17 '12 at 15:30 Omri 359 3 13 3 Convexity of the function $tmapsto tlog t$. – Did Jun 17 '12 at 15:33 In addition, the convexity properties require the coefficients in the linear combination sum 1. Then, as p(x,y) is a probability distribution, it fullfits such condition. – Francisco Javier Delgado Ceped Aug 10 at 18:44 add a comment  |  up vote 10 down vote favorite 6 What is the simplest proof that mutual information is always non-negative? i.e., $I(X;Y)ge0$ probability-theory share | cite | improve this question edited Jun 17 ...
閱讀完整內容

Why am i infinitely getting the same tweet with the Twitter Search API?

圖片
up vote 0 down vote favorite My code workes perfectly for other queries, but for one query I am infinitely getting the same tweet. I can't understand what the problem is. API call: query='Allergic asthma OR Nonallergic asthma OR Occupational asthma OR EIB OR Exercise-induced bronchoconstriction OR Nocturnal asthma OR Cough-variant asthma' new_tweets = api.search(q=searchQuery, count=100, since_id=since_id, lang='en',tweet_mode='extended') if not new_tweets: print("No more tweets found") break for tweet in new_tweets: if True: print(jsonpickle.encode(tweet._json, unpicklable=False)) my_file = open('searchTweets.txt','a') my_file.write(jsonpickle.encode(tweet._json, unpicklable=False)+'n') my_file.close() else: continue Output in file: https://pastebin.com/JmRCsTeE These are the JSONs of the same Tweet. Other queries that work: Breast cancer OR Prostate cancer OR Colon cancer OR Lung cancer Type 2 dia...
閱讀完整內容