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Question: plot output of an integral

Question:plot output of an integral

mehdi jafari 754 Maple 2018
integration plotting
May 17 2021
2

how this integration can be computed and plotted? tnx in advance

 

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restart:Digits:=20:
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T := 10^(-6);
delta := 10;
m := 1;
alpha:= 75/10;
v := 65;
mu := 8;

1/1000000

  

10

  

1

  

15/2

  

65

  

8

 (1)
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z := sqrt((omega^2 - 4*m^2)/alpha^2 - v^2/alpha^2*(4 *delta/alpha*tan(theta)^2 - v^4/alpha^4*tan(theta)^4))

(2/135)*(81*omega^2-324-1825200*tan(theta)^2+1930723600*tan(theta)^4)^(1/2)

 (2)
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a := sec(theta)/sqrt(2)*sqrt((2 *delta)/alpha - v^2/alpha^2*tan(theta)^2 + z)

(1/90)*sec(theta)*2^(1/2)*(5400-152100*tan(theta)^2+30*(81*omega^2-324-1825200*tan(theta)^2+1930723600*tan(theta)^4)^(1/2))^(1/2)

 (3)
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f1 := 1/(exp(( omega/2 - mu)/T) + 1);
f2 := 1/(exp((- (omega/2) - mu)/T) + 1);

1/(exp(500000*omega-8000000)+1)

  

1/(exp(-500000*omega-8000000)+1)

 (4)
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A1 := evalf(-(f1 - f2)*abs(omega/(4*a*alpha*cos(theta)^2*(-delta+ a^2 *alpha* cos(theta)^2) + 2*a*v^2*sin(theta)^2 + 1/10000)))

-1.*(1/(exp(500000.*omega-8000000.)+1.)-1./(exp(-500000.*omega-8000000.)+1.))*abs(omega/(.47140452079103168293*sec(theta)*(5400.-152100.*tan(theta)^2+30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))^(1/2)*cos(theta)^2*(-10.+0.18518518518518518519e-2*sec(theta)^2*(5400.-152100.*tan(theta)^2+30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))*cos(theta)^2)+132.77894002280725736*sec(theta)*(5400.-152100.*tan(theta)^2+30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))^(1/2)*sin(theta)^2+0.10000000000000000000e-3))

 (5)
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b := sec(theta)/sqrt(2)*sqrt((2*delta)/alpha - v^2/alpha^2*tan(theta)^2 - z)

(1/90)*sec(theta)*2^(1/2)*(5400-152100*tan(theta)^2-30*(81*omega^2-324-1825200*tan(theta)^2+1930723600*tan(theta)^4)^(1/2))^(1/2)

 (6)
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f3 := 1/(exp(( omega/2 - mu)/T) + 1);
f4 := 1/(exp((- (omega/2) - mu)/T) + 1);

1/(exp(500000*omega-8000000)+1)

  

1/(exp(-500000*omega-8000000)+1)

 (7)
> 

A2 := evalf(-(f3 - f2)*abs(omega/(4*b*alpha*cos(theta)^2*(-delta+ b^2 *alpha* cos(theta)^2) + 2*b*v^2*sin(theta)^2 + 1/10000)))

-1.*(1/(exp(500000.*omega-8000000.)+1.)-1./(exp(-500000.*omega-8000000.)+1.))*abs(omega/(.47140452079103168293*sec(theta)*(5400.-152100.*tan(theta)^2-30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))^(1/2)*cos(theta)^2*(-10.+0.18518518518518518519e-2*sec(theta)^2*(5400.-152100.*tan(theta)^2-30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))*cos(theta)^2)+132.77894002280725736*sec(theta)*(5400.-152100.*tan(theta)^2-30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))^(1/2)*sin(theta)^2+0.10000000000000000000e-3))

 (8)
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plot(int(A1+A2,theta=0..2*Pi),omega=0..50);

Warning,  computation interrupted

  
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