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Help in applying the boundaries of an elliptic integral

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0

$begingroup$

I need urgent help in determining the final result of the definite integral:

$$int_0^2pileft (bcos(x) + sqrta^2 - b^2sin^2(x)right), mathrmdx.$$
I know, by using an online integral calculator, the indefinite integral gives:

$$|a| Eleft(xleft|fracb^2a^2right.right) + b sin(x) + C$$

But, since it is an elliptical integral (of the second kind with parameter $m=k^2$), which is out of the scope of the mathematics I have studied and been familiar with, I cannot literally do anything about it.

Could someone, acquainted with elliptic integrals, apply the boundaries of the integral for me, please?

Please, I need this so badly. Any help would be appreciated.

integration definite-integrals indefinite-integrals

share|cite|improve this question

edited Mar 28 at 21:49

Brian

1,320216

asked Mar 28 at 20:01

physicist bychoicephysicist bychoice

65

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You do not explain why it is "urgent" and why you "need this so badly". Could you please elaborate a bit on those points?
  $endgroup$
  – mickep
  Mar 28 at 20:11
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Because I need this integral in solving a physics problem for myself, which has to do with the Biot-Savart law and, in another problem, the magnetic force on a wire. It is an integral that I cannot deal with, since it is out of the scope of my maths. I abandoned the problem bacause I could not find anyone I know to perform the integral fully and online integral calculators could not determine the result of the definite integral, but I see I now need to complete it and it would be helpful to ask.
  $endgroup$
  – physicist bychoice
  Mar 28 at 20:21
  
  

  
  
  
  

add a comment | 

0

$begingroup$

I need urgent help in determining the final result of the definite integral:

$$int_0^2pileft (bcos(x) + sqrta^2 - b^2sin^2(x)right), mathrmdx.$$
I know, by using an online integral calculator, the indefinite integral gives:

$$|a| Eleft(xleft|fracb^2a^2right.right) + b sin(x) + C$$

But, since it is an elliptical integral (of the second kind with parameter $m=k^2$), which is out of the scope of the mathematics I have studied and been familiar with, I cannot literally do anything about it.

Could someone, acquainted with elliptic integrals, apply the boundaries of the integral for me, please?

Please, I need this so badly. Any help would be appreciated.

integration definite-integrals indefinite-integrals

share|cite|improve this question

edited Mar 28 at 21:49

Brian

1,320216

asked Mar 28 at 20:01

physicist bychoicephysicist bychoice

65

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You do not explain why it is "urgent" and why you "need this so badly". Could you please elaborate a bit on those points?
  $endgroup$
  – mickep
  Mar 28 at 20:11
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Because I need this integral in solving a physics problem for myself, which has to do with the Biot-Savart law and, in another problem, the magnetic force on a wire. It is an integral that I cannot deal with, since it is out of the scope of my maths. I abandoned the problem bacause I could not find anyone I know to perform the integral fully and online integral calculators could not determine the result of the definite integral, but I see I now need to complete it and it would be helpful to ask.
  $endgroup$
  – physicist bychoice
  Mar 28 at 20:21
  
  

  
  
  
  

add a comment | 

$begingroup$

I need urgent help in determining the final result of the definite integral:

$$int_0^2pileft (bcos(x) + sqrta^2 - b^2sin^2(x)right), mathrmdx.$$
I know, by using an online integral calculator, the indefinite integral gives:

$$|a| Eleft(xleft|fracb^2a^2right.right) + b sin(x) + C$$

But, since it is an elliptical integral (of the second kind with parameter $m=k^2$), which is out of the scope of the mathematics I have studied and been familiar with, I cannot literally do anything about it.

Could someone, acquainted with elliptic integrals, apply the boundaries of the integral for me, please?

Please, I need this so badly. Any help would be appreciated.

integration definite-integrals indefinite-integrals

share|cite|improve this question

edited Mar 28 at 21:49

Brian

1,320216

asked Mar 28 at 20:01

physicist bychoicephysicist bychoice

65

$endgroup$

share|cite|improve this question

edited Mar 28 at 21:49

Brian

1,320216

asked Mar 28 at 20:01

physicist bychoicephysicist bychoice

65

share|cite|improve this question

edited Mar 28 at 21:49

Brian

1,320216

asked Mar 28 at 20:01

physicist bychoicephysicist bychoice

65

edited Mar 28 at 21:49

Brian

1,320216

edited Mar 28 at 21:49

Brian

1,320216

asked Mar 28 at 20:01

physicist bychoicephysicist bychoice

65

asked Mar 28 at 20:01

physicist bychoicephysicist bychoice

65