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If I am integrating a function $f(y)$ with respect to $x$ but no actual $x$ variable, should I treat that function as a constant?

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0

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$begingroup$

I am trying to integrate $cos(y^2) dx$ from the bound $y^3$ to $y^3$. Since I am integrating with respect to $x$ and not $y$, should I treat the function as a constant and integrate normally?

I tried putting it in online calculators such as symbolab but they keep changing $dx$ in to $dy$.

I would appreciate any help on this. Thanks!

integration

share|cite|improve this question

edited Mar 17 at 2:53

Rócherz

3,0013821

asked Mar 16 at 23:18

Niko HNiko H

73

$endgroup$

• 
  
  
  

  
  6
  

  
  
  
  
  
  

  
  $begingroup$
  The integral from $y^3$ to $y^3$ is $0$.
  $endgroup$
  – Kavi Rama Murthy
  Mar 16 at 23:20
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  You are correct. You treat the term as a constant with respect to $x$. You work more with integrals like this if you take multivariable calculus
  $endgroup$
  – WaveX
  Mar 16 at 23:27
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  As @KaviRamaMurthy pointed out, it doesn't matter, if the upper & lower bounds are the same then the integral has value zero.
  $endgroup$
  – copper.hat
  Mar 16 at 23:31
  

  
  
  
  

add a comment | 

0

1

$begingroup$

I am trying to integrate $cos(y^2) dx$ from the bound $y^3$ to $y^3$. Since I am integrating with respect to $x$ and not $y$, should I treat the function as a constant and integrate normally?

I tried putting it in online calculators such as symbolab but they keep changing $dx$ in to $dy$.

I would appreciate any help on this. Thanks!

integration

share|cite|improve this question

edited Mar 17 at 2:53

Rócherz

3,0013821

asked Mar 16 at 23:18

Niko HNiko H

73

$endgroup$

• 
  
  
  

  
  6
  

  
  
  
  
  
  

  
  $begingroup$
  The integral from $y^3$ to $y^3$ is $0$.
  $endgroup$
  – Kavi Rama Murthy
  Mar 16 at 23:20
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  You are correct. You treat the term as a constant with respect to $x$. You work more with integrals like this if you take multivariable calculus
  $endgroup$
  – WaveX
  Mar 16 at 23:27
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  As @KaviRamaMurthy pointed out, it doesn't matter, if the upper & lower bounds are the same then the integral has value zero.
  $endgroup$
  – copper.hat
  Mar 16 at 23:31
  

  
  
  
  

add a comment | 

$begingroup$

I am trying to integrate $cos(y^2) dx$ from the bound $y^3$ to $y^3$. Since I am integrating with respect to $x$ and not $y$, should I treat the function as a constant and integrate normally?

I tried putting it in online calculators such as symbolab but they keep changing $dx$ in to $dy$.

I would appreciate any help on this. Thanks!

integration

share|cite|improve this question

edited Mar 17 at 2:53

Rócherz

3,0013821

asked Mar 16 at 23:18

Niko HNiko H

73

$endgroup$

share|cite|improve this question

edited Mar 17 at 2:53

Rócherz

3,0013821

asked Mar 16 at 23:18

Niko HNiko H

73

share|cite|improve this question

edited Mar 17 at 2:53

Rócherz

3,0013821

asked Mar 16 at 23:18

Niko HNiko H

73

edited Mar 17 at 2:53

Rócherz

3,0013821

edited Mar 17 at 2:53

Rócherz

3,0013821

asked Mar 16 at 23:18

Niko HNiko H

73

asked Mar 16 at 23:18

Niko HNiko H

73