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Calculate the following integral: $int_0^2pi sqrtcos^2t + 9sin^2t, dt$

1

$begingroup$

I have the following integral:
$$int_0^2pi sqrtcos^2t + 9sin^2t, dt$$

I used $cos^2t + sin^2t=1$ and $2sin^2t=1-cos2t$ so I got:
$$int_0^2pi sqrt5-4cos2t , dt$$

but now I don't know how to continue with the solution.

calculus integration

share|cite|improve this question

edited Mar 26 at 18:15

Thomas Shelby

4,7832727

asked Mar 26 at 18:13

Dr.MathematicsDr.Mathematics

516

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  This looks like the perimeter of an ellipse which usually cannot be determined exactly.
  $endgroup$
  – Peter Foreman
  Mar 26 at 18:15
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  see complete elliptic integral of 2nd kind
  $endgroup$
  – achille hui
  Mar 26 at 18:18
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Wikipedia also explains how one might compute the circumference of an ellipse on this page
  $endgroup$
  – Omnomnomnom
  Mar 26 at 18:19
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  According to the google plugin, the answer is about $13.36$.
  $endgroup$
  – Omnomnomnom
  Mar 26 at 18:19
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I had to calculate the length of the curve $(sint, 3cost)$ for these $t$, that's why I got the integral. I don't know why our teacher give us this exercise since I am on my second semester at university and I don't really know what "elliptic integral of 2nd kind" is.
  $endgroup$
  – Dr.Mathematics
  Mar 26 at 19:05
  

  
  
  
  

 | 
show 1 more comment

1

$begingroup$

I have the following integral:
$$int_0^2pi sqrtcos^2t + 9sin^2t, dt$$

I used $cos^2t + sin^2t=1$ and $2sin^2t=1-cos2t$ so I got:
$$int_0^2pi sqrt5-4cos2t , dt$$

but now I don't know how to continue with the solution.

calculus integration

share|cite|improve this question

edited Mar 26 at 18:15

Thomas Shelby

4,7832727

asked Mar 26 at 18:13

Dr.MathematicsDr.Mathematics

516

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  This looks like the perimeter of an ellipse which usually cannot be determined exactly.
  $endgroup$
  – Peter Foreman
  Mar 26 at 18:15
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  see complete elliptic integral of 2nd kind
  $endgroup$
  – achille hui
  Mar 26 at 18:18
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Wikipedia also explains how one might compute the circumference of an ellipse on this page
  $endgroup$
  – Omnomnomnom
  Mar 26 at 18:19
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  According to the google plugin, the answer is about $13.36$.
  $endgroup$
  – Omnomnomnom
  Mar 26 at 18:19
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I had to calculate the length of the curve $(sint, 3cost)$ for these $t$, that's why I got the integral. I don't know why our teacher give us this exercise since I am on my second semester at university and I don't really know what "elliptic integral of 2nd kind" is.
  $endgroup$
  – Dr.Mathematics
  Mar 26 at 19:05
  

  
  
  
  

 | 
show 1 more comment

$begingroup$

I have the following integral:
$$int_0^2pi sqrtcos^2t + 9sin^2t, dt$$

I used $cos^2t + sin^2t=1$ and $2sin^2t=1-cos2t$ so I got:
$$int_0^2pi sqrt5-4cos2t , dt$$

but now I don't know how to continue with the solution.

calculus integration

share|cite|improve this question

edited Mar 26 at 18:15

Thomas Shelby

4,7832727

asked Mar 26 at 18:13

Dr.MathematicsDr.Mathematics

516

$endgroup$

share|cite|improve this question

edited Mar 26 at 18:15

Thomas Shelby

4,7832727

asked Mar 26 at 18:13

Dr.MathematicsDr.Mathematics

516

share|cite|improve this question

edited Mar 26 at 18:15

Thomas Shelby

4,7832727

asked Mar 26 at 18:13

Dr.MathematicsDr.Mathematics

516

edited Mar 26 at 18:15

Thomas Shelby

4,7832727

edited Mar 26 at 18:15

Thomas Shelby

4,7832727

asked Mar 26 at 18:13

Dr.MathematicsDr.Mathematics

516

asked Mar 26 at 18:13

Dr.MathematicsDr.Mathematics

516