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Evaluating trigonometric integral using contour integration

-1

$begingroup$

$$
int_0^pileft(fracmleftright)^2d(wt)
$$

Does anyone know how to calculate this integral using complex integrals or any other method?. kindly help me.

complex-analysis

share|cite|improve this question

edited Mar 31 at 18:01

user

6,56511031

asked Mar 31 at 17:08

GNANAPATHY GGNANAPATHY G

11

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What is the variable running from $0$ to $pi $? If it is $wt $ what was the reason to use a two-letter code for it?
  $endgroup$
  – user
  Mar 31 at 18:05
  
  

  
  
  
  

add a comment | 

-1

$begingroup$

$$
int_0^pileft(fracmleftright)^2d(wt)
$$

Does anyone know how to calculate this integral using complex integrals or any other method?. kindly help me.

complex-analysis

share|cite|improve this question

edited Mar 31 at 18:01

user

6,56511031

asked Mar 31 at 17:08

GNANAPATHY GGNANAPATHY G

11

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What is the variable running from $0$ to $pi $? If it is $wt $ what was the reason to use a two-letter code for it?
  $endgroup$
  – user
  Mar 31 at 18:05
  
  

  
  
  
  

add a comment | 

$begingroup$

$$
int_0^pileft(fracmleftright)^2d(wt)
$$

Does anyone know how to calculate this integral using complex integrals or any other method?. kindly help me.

complex-analysis

share|cite|improve this question

edited Mar 31 at 18:01

user

6,56511031

asked Mar 31 at 17:08

GNANAPATHY GGNANAPATHY G

11

$endgroup$

share|cite|improve this question

edited Mar 31 at 18:01

user

6,56511031

asked Mar 31 at 17:08

GNANAPATHY GGNANAPATHY G

11

share|cite|improve this question

edited Mar 31 at 18:01

user

6,56511031

asked Mar 31 at 17:08

GNANAPATHY GGNANAPATHY G

11

edited Mar 31 at 18:01

user

6,56511031

edited Mar 31 at 18:01

user

6,56511031

asked Mar 31 at 17:08

GNANAPATHY GGNANAPATHY G

11

asked Mar 31 at 17:08

GNANAPATHY GGNANAPATHY G

11

1 Answer
1

active

oldest

votes

0

$begingroup$

Is $wt$ the variable, or is it $t$ with $w$ constant?

If $0 < wt < pi$, $sin(wt) > 0$ so you don't need the absolute values.
If you integrate over an interval where $sin(wt)$ changes sign, you'll want to
split it up into cases where $sin(wt) > 0$ and $< 0$.

The integrals of $(m sin(wt)/(1 - m sin(wt)))^2$ and $(m sin(wt)/(1 + m sin(wt)))^2$ can be done in closed form. Try the substitution $u = tan(wt/2)$.
But you'll want to ensure the denominator is not $0$ on the interval

share|cite|improve this answer

answered Mar 31 at 17:22

Robert IsraelRobert Israel

331k23221478

$endgroup$

add a comment | 

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0

$begingroup$

Is $wt$ the variable, or is it $t$ with $w$ constant?

If $0 < wt < pi$, $sin(wt) > 0$ so you don't need the absolute values.
If you integrate over an interval where $sin(wt)$ changes sign, you'll want to
split it up into cases where $sin(wt) > 0$ and $< 0$.

The integrals of $(m sin(wt)/(1 - m sin(wt)))^2$ and $(m sin(wt)/(1 + m sin(wt)))^2$ can be done in closed form. Try the substitution $u = tan(wt/2)$.
But you'll want to ensure the denominator is not $0$ on the interval

share|cite|improve this answer

answered Mar 31 at 17:22

Robert IsraelRobert Israel

331k23221478

$endgroup$

add a comment | 

0

$begingroup$

Is $wt$ the variable, or is it $t$ with $w$ constant?

If $0 < wt < pi$, $sin(wt) > 0$ so you don't need the absolute values.
If you integrate over an interval where $sin(wt)$ changes sign, you'll want to
split it up into cases where $sin(wt) > 0$ and $< 0$.

The integrals of $(m sin(wt)/(1 - m sin(wt)))^2$ and $(m sin(wt)/(1 + m sin(wt)))^2$ can be done in closed form. Try the substitution $u = tan(wt/2)$.
But you'll want to ensure the denominator is not $0$ on the interval

share|cite|improve this answer

answered Mar 31 at 17:22

Robert IsraelRobert Israel

331k23221478

$endgroup$

add a comment | 

$begingroup$

Is $wt$ the variable, or is it $t$ with $w$ constant?

If $0 < wt < pi$, $sin(wt) > 0$ so you don't need the absolute values.
If you integrate over an interval where $sin(wt)$ changes sign, you'll want to
split it up into cases where $sin(wt) > 0$ and $< 0$.

The integrals of $(m sin(wt)/(1 - m sin(wt)))^2$ and $(m sin(wt)/(1 + m sin(wt)))^2$ can be done in closed form. Try the substitution $u = tan(wt/2)$.
But you'll want to ensure the denominator is not $0$ on the interval

share|cite|improve this answer

answered Mar 31 at 17:22

Robert IsraelRobert Israel

331k23221478

$endgroup$

share|cite|improve this answer

answered Mar 31 at 17:22

Robert IsraelRobert Israel

331k23221478

answered Mar 31 at 17:22

Robert IsraelRobert Israel

331k23221478

answered Mar 31 at 17:22

Robert IsraelRobert Israel

331k23221478