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Closed form solution to $int_0^pi/4frace^icsqrt1+ br^2(theta)sqrt1+ br^2(theta),dtheta$

Closed form solution $int_-pi ^pi fraccos ^m(theta -psi )cos ^2(theta -varphi ) , mathrm dtheta$Closed Form for $int_0^1 fraclog(x)sqrt1-x^2sqrtx^2+2+2sqrt2dx$General closed form of $int_0^theta_o dfrac1sqrtcos theta-cos theta_o dtheta$Closed form of $int_0^pi/2 fracarctan^2 (sin^2 theta)sin^2 theta,dtheta$Choosing the correct branch in $int fraca-cos(theta)b-cos(theta) dtheta$Calculate $int_0^1fraccos(arctan x)sqrtxdx$How to evaluate $int_0^2pifrac1-alphacosthetar'^3dtheta$Finding $int_0^2pi sqrtx + frac14x; dx $Is there a closed form solution of this definite integralEvaluate $int_0^fracpi2 frac1sqrta^2 cos^2 theta+b^2 sin^2 theta d theta$

1

$begingroup$

Is there closed form solution to this integral
$$int_0^pi/4frace^icsqrt1+ br^2(theta)sqrt1+ br^2(theta),dtheta$$

$r(theta)=fracacos(theta)$ is radius vector from the origin tracing square with side 2a (0,45 deg).

$c=$ constant, $b=$ constant.

integration definite-integrals polar-coordinates line-integrals trigonometric-integrals

share|cite|improve this question

edited Mar 17 at 21:54

user591849

asked Mar 15 at 16:50

user591849user591849

133

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Interesting question. What have you attempted so far? Also, what are $b$ and $c$?
  $endgroup$
  – Mohammad Zuhair Khan
  Mar 15 at 16:53
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Hint: What does differentiating the integral with respect to $c$ give you?
  $endgroup$
  – Darkrai
  Mar 15 at 17:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks. What substitution would solve the integral after differentiating.
  $endgroup$
  – user591849
  Mar 16 at 8:18
  

  
  
  
  

add a comment | 

1

$begingroup$

Is there closed form solution to this integral
$$int_0^pi/4frace^icsqrt1+ br^2(theta)sqrt1+ br^2(theta),dtheta$$

$r(theta)=fracacos(theta)$ is radius vector from the origin tracing square with side 2a (0,45 deg).

$c=$ constant, $b=$ constant.

integration definite-integrals polar-coordinates line-integrals trigonometric-integrals

share|cite|improve this question

edited Mar 17 at 21:54

user591849

asked Mar 15 at 16:50

user591849user591849

133

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Interesting question. What have you attempted so far? Also, what are $b$ and $c$?
  $endgroup$
  – Mohammad Zuhair Khan
  Mar 15 at 16:53
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Hint: What does differentiating the integral with respect to $c$ give you?
  $endgroup$
  – Darkrai
  Mar 15 at 17:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks. What substitution would solve the integral after differentiating.
  $endgroup$
  – user591849
  Mar 16 at 8:18
  

  
  
  
  

add a comment | 

$begingroup$

Is there closed form solution to this integral
$$int_0^pi/4frace^icsqrt1+ br^2(theta)sqrt1+ br^2(theta),dtheta$$

$r(theta)=fracacos(theta)$ is radius vector from the origin tracing square with side 2a (0,45 deg).

$c=$ constant, $b=$ constant.

integration definite-integrals polar-coordinates line-integrals trigonometric-integrals

share|cite|improve this question

edited Mar 17 at 21:54

user591849

asked Mar 15 at 16:50

user591849user591849

133

$endgroup$

share|cite|improve this question

edited Mar 17 at 21:54

user591849

asked Mar 15 at 16:50

user591849user591849

133

share|cite|improve this question

edited Mar 17 at 21:54

user591849

asked Mar 15 at 16:50

user591849user591849

133

asked Mar 15 at 16:50

user591849user591849

133

asked Mar 15 at 16:50

user591849user591849

133