Mfcttrf

Why can't I see bouncing of a switch on an oscilloscope?

Why is Minecraft giving an OpenGL error?

Can an x86 CPU running in real mode be considered to be basically an 8086 CPU?

Did Shadowfax go to Valinor?

I'm flying to France today and my passport expires in less than 2 months

Is it unprofessional to ask if a job posting on GlassDoor is real?

What typically incentivizes a professor to change jobs to a lower ranking university?

Fully-Firstable Anagram Sets

Watching something be written to a file live with tail

Important Resources for Dark Age Civilizations?

tikz convert color string to hex value

What's the point of deactivating Num Lock on login screens?

Approximately how much travel time was saved by the opening of the Suez Canal in 1869?

How to efficiently unroll a matrix by value with numpy?

Today is the Center

How to format long polynomial?

Has there ever been an airliner design involving reducing generator load by installing solar panels?

RSA: Danger of using p to create q

What does the "remote control" for a QF-4 look like?

dbcc cleantable batch size explanation

NMaximize is not converging to a solution

How old can references or sources in a thesis be?

Add text to same line using sed

Is it legal for company to use my work email to pretend I still work there?

Definite integral giving negative value as a result?

Why do I get a negative value for this integral?Solving a definite integralReal integral giving a complex resultProgression from indefinite integral to definite integral - $int_0^2pifrac15-3cos x dx$Calculation of definite integralWithout calculating the integral decide if integral is positive or negative / which integral is bigger?Definite integral of absolute value function?Variable substitution in definite integralDefinite integral over singularityInner Product, Definite Integral

4

$begingroup$

I want to calculate definite integral

$$int_-2^-1 frac1x^2e^frac1x dx = Omega$$

$$int frac1x^2e^frac1x dx=-e^frac1x+C$$

so:

$$Omega = [-e^frac1-2]-[-e^frac1-1]=-frac1sqrte + frac1e$$

which is a negative value. I believe it should be positive.

What went wrong in the process?

calculus integration definite-integrals

share|cite|improve this question

edited 6 hours ago

Eevee Trainer

9,93831740

asked 6 hours ago

wenoweno

39611

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  How exactly did you go about calculating the antiderivative? Wolfram Alpha gives a much different result.
  $endgroup$
  – Eevee Trainer
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Your antiderivative is completely incorrect: The derivative of $e^1/x^2$ is $e^1/x^2 / (-x^3)$. The red flag that you found is indeed a correct one, and shows that your answer cannot be right. This is a good thing to check.
  $endgroup$
  – T. Bongers
  6 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks. I have fixed it now. I meant $int frac1x^2 e^frac1xdx$.
  $endgroup$
  – weno
  6 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  5
  

  
  
  
  
  
  

  
  $begingroup$
  You flipped the interval's endpoints. $-2<-1$
  $endgroup$
  – mr_e_man
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  And just to confirm, taking account of @mr_e_man’s comment above, your work seems correct.
  $endgroup$
  – Lubin
  6 hours ago
  

  
  
  
  

 | 
show 2 more comments

4

$begingroup$

I want to calculate definite integral

$$int_-2^-1 frac1x^2e^frac1x dx = Omega$$

$$int frac1x^2e^frac1x dx=-e^frac1x+C$$

so:

$$Omega = [-e^frac1-2]-[-e^frac1-1]=-frac1sqrte + frac1e$$

which is a negative value. I believe it should be positive.

What went wrong in the process?

calculus integration definite-integrals

share|cite|improve this question

edited 6 hours ago

Eevee Trainer

9,93831740

asked 6 hours ago

wenoweno

39611

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  How exactly did you go about calculating the antiderivative? Wolfram Alpha gives a much different result.
  $endgroup$
  – Eevee Trainer
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Your antiderivative is completely incorrect: The derivative of $e^1/x^2$ is $e^1/x^2 / (-x^3)$. The red flag that you found is indeed a correct one, and shows that your answer cannot be right. This is a good thing to check.
  $endgroup$
  – T. Bongers
  6 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks. I have fixed it now. I meant $int frac1x^2 e^frac1xdx$.
  $endgroup$
  – weno
  6 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  5
  

  
  
  
  
  
  

  
  $begingroup$
  You flipped the interval's endpoints. $-2<-1$
  $endgroup$
  – mr_e_man
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  And just to confirm, taking account of @mr_e_man’s comment above, your work seems correct.
  $endgroup$
  – Lubin
  6 hours ago
  

  
  
  
  

 | 
show 2 more comments

$begingroup$

I want to calculate definite integral

$$int_-2^-1 frac1x^2e^frac1x dx = Omega$$

$$int frac1x^2e^frac1x dx=-e^frac1x+C$$

so:

$$Omega = [-e^frac1-2]-[-e^frac1-1]=-frac1sqrte + frac1e$$

which is a negative value. I believe it should be positive.

What went wrong in the process?

calculus integration definite-integrals

share|cite|improve this question

edited 6 hours ago

Eevee Trainer

9,93831740

asked 6 hours ago

wenoweno

39611

$endgroup$

share|cite|improve this question

edited 6 hours ago

Eevee Trainer

9,93831740

asked 6 hours ago

wenoweno

39611

share|cite|improve this question

edited 6 hours ago

Eevee Trainer

9,93831740

asked 6 hours ago

wenoweno

39611

edited 6 hours ago

Eevee Trainer

9,93831740

edited 6 hours ago

Eevee Trainer

9,93831740

asked 6 hours ago

wenoweno

39611

asked 6 hours ago

wenoweno

39611

1 Answer
1

active

oldest

votes

4

$begingroup$

What you effectively did was swap the order of evaluation for the fundamental theorem of calculus. Recall:

$$int_a^b f(x)dx = F(b) - F(a)$$

when the antiderivative of $f$ is $F$. You instead have $F(a) - F(b)$ ($a=-2,b=-1$) in this case. The end result is merely a sign error - you have precisely the negative of the answer which you should expect.

share|cite|improve this answer

answered 6 hours ago

Eevee TrainerEevee Trainer

9,93831740

$endgroup$

add a comment | 

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',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name

Email

Required, but never shown

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3176540%2fdefinite-integral-giving-negative-value-as-a-result%23new-answer', 'question_page');

);

Post as a guest

Name

Email

Required, but never shown

4

$begingroup$

What you effectively did was swap the order of evaluation for the fundamental theorem of calculus. Recall:

$$int_a^b f(x)dx = F(b) - F(a)$$

when the antiderivative of $f$ is $F$. You instead have $F(a) - F(b)$ ($a=-2,b=-1$) in this case. The end result is merely a sign error - you have precisely the negative of the answer which you should expect.

share|cite|improve this answer

answered 6 hours ago

Eevee TrainerEevee Trainer

9,93831740

$endgroup$

add a comment | 

4

$begingroup$

What you effectively did was swap the order of evaluation for the fundamental theorem of calculus. Recall:

$$int_a^b f(x)dx = F(b) - F(a)$$

when the antiderivative of $f$ is $F$. You instead have $F(a) - F(b)$ ($a=-2,b=-1$) in this case. The end result is merely a sign error - you have precisely the negative of the answer which you should expect.

share|cite|improve this answer

answered 6 hours ago

Eevee TrainerEevee Trainer

9,93831740

$endgroup$

add a comment | 

$begingroup$

What you effectively did was swap the order of evaluation for the fundamental theorem of calculus. Recall:

$$int_a^b f(x)dx = F(b) - F(a)$$

when the antiderivative of $f$ is $F$. You instead have $F(a) - F(b)$ ($a=-2,b=-1$) in this case. The end result is merely a sign error - you have precisely the negative of the answer which you should expect.

share|cite|improve this answer

answered 6 hours ago

Eevee TrainerEevee Trainer

9,93831740

$endgroup$

share|cite|improve this answer

answered 6 hours ago

Eevee TrainerEevee Trainer

9,93831740

answered 6 hours ago

Eevee TrainerEevee Trainer

9,93831740

answered 6 hours ago

Eevee TrainerEevee Trainer

9,93831740