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m_goldberg
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Determining the range of parameters that yield real values for a certain NIntegrate form

I have specified just one set of $s$ and $g$ values that yields a real value for the NIntegrateNIntegrate below. It is possible that some $s$,$g$$s,g$ combination can give rise to an imaginary output.I I would like to know the method of determining the whole range of ${s,g}$$s,g$ values that give rise to real value outcome for the Integration belowintegration. A regionplot mayregion plot might be useful, but nevertheless a neat way of doing this will be appreciated.

s = 1.1; 
g = 0.1; 

NIntegrate[
  (p^2* Sqrt[1 - (2*p)/(-g + p*(1 + p))])/(-1 + (p/g)*(p - 1)) - 
  p^2/((1 + p/g)*(1 + p))*Sqrt[1 - (2*p)/(g + p*(1 + p))]), 
  {p, s, 1000}]

Determining the range of parameters that yield real values for NIntegrate

I have specified just one set of $s$ and $g$ that yields a real value for the NIntegrate below. It is possible that some $s$,$g$ combination can give rise to an imaginary output.I would like to know the method of determining the whole range of ${s,g}$ values that give rise to real value outcome for the Integration below. A regionplot may be useful, but nevertheless a neat way of doing this will be appreciated.

s = 1.1; 
g = 0.1; 

NIntegrate[(p^2* Sqrt[1 - (2*p)/(-g + p*(1 + p))])/(-1 + (p/g)*(p - 1)) - p^2/((1 + p/g)*(1 + p))*Sqrt[1 - (2*p)/(g + p*(1 + p))]), {p, s, 1000}]

Determining the range of parameters that yield real values for a certain NIntegrate form

I have specified just one set of $s$ and $g$ values that yields a real value for the NIntegrate below. It is possible that some $s,g$ combination can give rise to an imaginary output. I would like to know the method of determining the whole range of $s,g$ values that give rise to real value outcome for the integration. A region plot might be useful, but nevertheless a neat way of doing this will be appreciated.

s = 1.1; 
g = 0.1; 

NIntegrate[
  (p^2* Sqrt[1 - (2*p)/(-g + p*(1 + p))])/(-1 + (p/g)*(p - 1)) - 
  p^2/((1 + p/g)*(1 + p))*Sqrt[1 - (2*p)/(g + p*(1 + p))]), 
  {p, s, 1000}]
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thils
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I have specified just one set of $s$ and $g$ that yields a real value for the NIntegrate below. It is possible that some $s$,$g$ combination can give rise to an imaginary output.I would like to know the the the method of determining the whole range of ${s,g}$ values that give rise to real value outcome for the Integration below. A regionplot may be useful, but nevertheless a neat way of doing this will be appreciated.

s = 1.1; 
g = 0.1; 

NIntegrate[(p^2* Sqrt[1 - (2*p)/(-g + p*(1 + p))])/(-1 + (p/g)*(p - 1)) - p^2/((1 + p/g)*(1 + p))*Sqrt[1 - (2*p)/(g + p*(1 + p))]), {p, s, 1000}]

I have specified just one set of $s$ and $g$ that yields a real value for the NIntegrate below. It is possible that some $s$,$g$ combination can give rise to an imaginary output.I would like to know the the method of determining the whole range of ${s,g}$ values that give rise to real value outcome for the Integration below. A regionplot may be useful, but nevertheless a neat way of doing this will be appreciated.

s = 1.1; 
g = 0.1; 

NIntegrate[(p^2* Sqrt[1 - (2*p)/(-g + p*(1 + p))])/(-1 + (p/g)*(p - 1)) - p^2/((1 + p/g)*(1 + p))*Sqrt[1 - (2*p)/(g + p*(1 + p))]), {p, s, 1000}]

I have specified just one set of $s$ and $g$ that yields a real value for the NIntegrate below. It is possible that some $s$,$g$ combination can give rise to an imaginary output.I would like to know the method of determining the whole range of ${s,g}$ values that give rise to real value outcome for the Integration below. A regionplot may be useful, but nevertheless a neat way of doing this will be appreciated.

s = 1.1; 
g = 0.1; 

NIntegrate[(p^2* Sqrt[1 - (2*p)/(-g + p*(1 + p))])/(-1 + (p/g)*(p - 1)) - p^2/((1 + p/g)*(1 + p))*Sqrt[1 - (2*p)/(g + p*(1 + p))]), {p, s, 1000}]
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thils
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Determining the range of parameters whichthat yield real values for NIntegrate

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thils
  • 3.3k
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