如何做双重积分包括符号积分??

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gourav pandey
gourav pandey 2021年8月16日
clc;
清晰;
所有;
信谊Ps2 Ps3 Ps4 Qc2 Qc3 Qc4 Qs2 Qs3 Qs4
a1=1;
h1 = 5;
temp = @(θ,ω)ω。^ 2。* exp (abs(ω)。* (cos(θ)+ 5))* ((Qs2。*((28222125408961305。* 2 ^(1. / 2)。*π。^(1. / 2)。* exp(ω)。/ 4503599627370496 +(141110627044806525。* 2 ^(1. / 2)^ 2。*π*ω。^(1. / 2)。* exp(ω)。*(3。/ω+ 3. /ω。^ 2 + 1))。/ 18014398509481984 -(84666376226883915 * 2。^(1. / 2)。*ω。*π。^(1. / 2)。* exp(ω)。*(1。/ω+ 1))。/ 4503599627370496 -(9407375136320435 * 2。^(1. / 2)。*ω^ 3。*π。^(1. / 2)。* exp(ω)。*(6。/ω+ 15. /ω。^ 2 + 15. /ω。^ 3 + 1) / 18014398509481984) + Pc2。*((9407375136320435。*ω。^(5. / 2)*((5 * 2。^(1. / 2)。*π。^(1. / 2)。* exp(ω)。*(3。/ω+ 3. /ω。^ 2 + 1))。/(2.*omega1.^(1./2)) + (2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./2))./18014398509481984 - (28222125408961305.*omega1.^(3./2).*((2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1))./2 + (3.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./(2.*omega1.^(1./2))))./18014398509481984 - (28222125408961305.*2.^(1./2).*pi.^(1./2).*exp(-omega1))./4503599627370496 + (28222125408961305.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./36028797018963968 + (84666376226883915.*2.^(1./2).*omega1.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./18014398509481984 - (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./36028797018963968) + Q_n.*pi.*exp(-omega1).*((5.*omega1)./2 + 5./2) - (5.*pi.*P_t.*omega1.*exp(-omega1))./2)./omega1.^2 - (cos(theta) + 5).*((Qs2.*((28222125408961305.*omega1.^(3./2).*((5.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./(2.*omega1.^(1./2)) - (2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./2))./4503599627370496 + (28222125408961305.*omega1.^(1./2).*((2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./2 - (3.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./(2.*omega1.^(1./2))))./2251799813685248 + (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./18014398509481984 - (28222125408961305.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./18014398509481984) - (5.*pi.*P_t.*omega1.*exp(-omega1))./2 + (5.*pi.*Q_n.*omega1.*exp(-omega1))./2)./omega1 - (abs(omega1).*(Qs2.*((28222125408961305.*2.^(1./2).*pi.^(1./2).*exp(-omega1))./4503599627370496 + (141110627044806525.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./18014398509481984 - (84666376226883915.*2.^(1./2).*omega1.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./4503599627370496 - (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./18014398509481984) + Pc2.*((9407375136320435.*omega1.^(5./2).*((5.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./(2.*omega1.^(1./2)) + (2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./2))./18014398509481984 - (28222125408961305.*omega1.^(3./2).*((2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1))./2 + (3.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./(2.*omega1.^(1./2))))./18014398509481984 - (28222125408961305.*2.^(1./2).*pi.^(1./2).*exp(-omega1))./4503599627370496 + (28222125408961305.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./36028797018963968 + (84666376226883915.*2.^(1./2).*omega1.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./18014398509481984 - (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./36028797018963968) + Q_n.*pi.*exp(-omega1).*((5.*omega1)./2 + 5./2) - (5.*pi.*P_t.*omega1.*exp(-omega1))./2))./omega1.^2))
Fun = integral2(@(theta, ω) (temp(theta, ω).*cos(theta .*a1.*sin(theta))),0,2*pi,0,inf)
%%%%%%%%%%% 请帮助……我是matlab的初学者。我试着用"double"但是出错了。请帮助
%%%%%%%%%提前谢谢你

接受的答案

沃尔特·罗伯森
沃尔特·罗伯森 2021年8月16日
当要集成的表达式包含未解析的符号变量时,无法使用integral()或integral2()。integral()和integral2()是严格的数值积分。
下面这些可能需要一段时间。您可以在相当合理的时间内完成result_inner,但最后一步并不快。
信谊Ps2 Ps3 Ps4 Qc2 Qc3 Qc4 Qs2 Qs3 Qs4
假设(θ>=0&omega1>=0)
a1=1;
h1 = 5;
temp_sym=简化(str2sym(“ω^。2。* exp (abs(ω)。* (cos(θ)+ 5))* ((Qs2。*((28222125408961305。* 2 ^(1. / 2)。*π。^(1. / 2)。* exp(ω)。/ 4503599627370496 +(141110627044806525。* 2 ^(1. / 2)^ 2。*π*ω。^(1. / 2)。* exp(ω)。*(3。/ω+ 3. /ω。^ 2 + 1))。/ 18014398509481984 -(84666376226883915 * 2。^(1. / 2)。*ω。*π。^(1. / 2)。* exp(ω)。*(1。/ω+ 1))。/ 4503599627370496 -(9407375136320435 * 2。^(1. / 2)。*ω^ 3。*π。^(1. / 2)。* exp(ω)。*(6。/ω+ 15. /ω。^ 2 + 15. /ω。^ 3 + 1) / 18014398509481984) + Pc2。*((9407375136320435。*ω。^(5. / 2)*((5 * 2。^(1. / 2)。*π。^(1. / 2)。* exp(ω)。*(3。/ω+ 3. /ω。^ 2 + 1))。/(2.*omega1.^(1./2)) + (2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./2))./18014398509481984 - (28222125408961305.*omega1.^(3./2).*((2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1))./2 + (3.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./(2.*omega1.^(1./2))))./18014398509481984 - (28222125408961305.*2.^(1./2).*pi.^(1./2).*exp(-omega1))./4503599627370496 + (28222125408961305.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./36028797018963968 + (84666376226883915.*2.^(1./2).*omega1.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./18014398509481984 - (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./36028797018963968) + Q_n.*pi.*exp(-omega1).*((5.*omega1)./2 + 5./2) - (5.*pi.*P_t.*omega1.*exp(-omega1))./2)./omega1.^2 - (cos(theta) + 5).*((Qs2.*((28222125408961305.*omega1.^(3./2).*((5.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./(2.*omega1.^(1./2)) - (2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./2))./4503599627370496 + (28222125408961305.*omega1.^(1./2).*((2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./2 - (3.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./(2.*omega1.^(1./2))))./2251799813685248 + (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./18014398509481984 - (28222125408961305.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./18014398509481984) - (5.*pi.*P_t.*omega1.*exp(-omega1))./2 + (5.*pi.*Q_n.*omega1.*exp(-omega1))./2)./omega1 - (abs(omega1).*(Qs2.*((28222125408961305.*2.^(1./2).*pi.^(1./2).*exp(-omega1))./4503599627370496 + (141110627044806525.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./18014398509481984 - (84666376226883915.*2.^(1./2).*omega1.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./4503599627370496 - (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./18014398509481984) + Pc2.*((9407375136320435.*omega1.^(5./2).*((5.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./(2.*omega1.^(1./2)) + (2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./2))./18014398509481984 - (28222125408961305.*omega1.^(3./2).*((2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1))./2 + (3.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./(2.*omega1.^(1./2))))./18014398509481984 - (28222125408961305.*2.^(1./2).*pi.^(1./2).*exp(-omega1))./4503599627370496 + (28222125408961305.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./36028797018963968 + (84666376226883915.*2.^(1./2).*omega1.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./18014398509481984 - (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./36028797018963968) + Q_n.*pi.*exp(-omega1).*((5.*omega1)./2 + 5./2) - (5.*pi.*P_t.*omega1.*exp(-omega1))./2))./omega1.^2))'))
内部=(温度sym.*cos(ω1.*a1.*sin(θ)))
内部sym=简化(内部)
结果内部=int(内部符号,θ,0,2*pi)
结果=int(结果\u内部,omega1,0,inf)
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答案(1)

马特·J
马特·J 2021年8月16日
编辑:马特·J 2021年8月16日
如果要对符号表达式积分,应该使用 int ()
你应该删除“ @(θ,ω) “从临时工的定义来看。如果有必要,把它放在那里是没有意义的 西塔 ω 是象征性的。
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gourav pandey
gourav pandey 2021年8月16日
和是函数柄。谢谢马特,我会改的。谢谢你!

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