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qrr_xmc: ½ð±Ò+4, ¡ï¡ï¡ïºÜÓаïÖú 2015-11-14 16:43:22
Áîx=[(b-a)/2]*sin(t)+(a+b)/2,t ´Ó-pi/2µ½pi/2
2Â¥2015-11-14 12:33:25
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qrr_xmc: ½ð±Ò+4, ¡ï¡ï¡ïºÜÓаïÖú 2015-11-14 16:43:37
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>> syms x a b
>> int(sqrt((b-x)*(x-a))/2/pi/x,x,a,b)
Warning: Explicit integral could not be found.
> In D:\Matlab\toolbox\symbolic\@sym\int.m at line 58

ans =

int(1/2*(-(-b+x)*(x-a))^(1/2)/pi/x,x = a .. b)
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qrr_xmc: ½ð±Ò+8, ¡ï¡ï¡ïºÜÓаïÖú 2015-11-14 16:41:37
Áîu=(b+a)/2+(b-a)/2*Sinu
ԭʽ=(b-a)^2/(8*¦Ð)Integral{[Cosu]^2/{(b+a)/2+(b-a)/2*Sinu}*du , -¦Ð/2 , ¦Ð/2}
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Ôò£ºCosu=(1-t^2)/(1+t^2) ,
      Sinu=2*t/(1+t^2)
       du=2*dt/(1+t^2)
ԭʽ=(b-a)^2/(8*¦Ð)*Integral{[u^4-2*u^2+1]*du/{[1+u^2]^2*{{u+(b-a)/[2*(b+a)]}^2+1-{(b-a)/[2*(b+a)]}^2}}, -1 , 1}
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{[u^4-2*u^2+1]*du/{[1+u^2]^2*{{u+(b-a)/[2*(b+a)]}^2+1-{(b-a)/[2*(b+a)]}^2}}= (A*u+B)/[1+u^2]^2+(C*u+D)/(1+u^2)+(E*u+F)/{{u+(b-a)/[2*(b+a)]}^2+1-{(b-a)/[2*(b+a)]}^2}}
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