MATLAB: Fn = c1/((lamda​^5)*((exp(​c2/(lamda*​T))) – 1)); I want to integrate this equation but getting Explicit Integral warning. here C1,C2,T are all unknown, integration has to be done in terms of lamda under the limits 0 to infinity. can anyone help me

spectral emissive power

fn = c1/((lamda^5)*((exp(c2/(lamda*T))) – 1)); I want to integrate this equation but getting Explicit Integral warning. Here C1,C2,T are all known, integration has to be done in terms of lamda under the limits 0 to infinity. can anyone help me

Best Answer

With the constants and the additional information, this runs:
C1 = 3.742E+8;
C2 = 1.439E+4;
E = @(L,T) C1./(L.^5 .* exp(C2./(L.*T)) - 1);
ET = @(T) integral(@(L) E(L,T), 0, Inf);
T = linspace(0, 310, 50);
for k1 = 1:length(T)
    ETT(k1) = ET(T(k1));
end
figure(1)
plot(T, ETT)
grid
xlabel('T (°K)')
ylabel('Spectral Blackbody Emmisive Power')
The loop is unavoidable.
I will let you determine if this does what you want.
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