Integration with piecewise function
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Hi! I have the following problem. I have a piecewise function and i need to integrate the function with the piecewise as variable. I have type the piecewise function (see pic) but don't know where to go from there.Your help in this regard is much appreciated. T' and T are the same. I have to determine the Pf (an integral) with Cv4 (a variable of S4) as piecewise function.
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Bjorn Gustavsson
2021년 3월 19일
Doesn't this work:
C_v4 = @(T) 0.0516*T.^3.*double(T<=0.6) + .432*T.^6.7.*double(0.6<T).*double(T<1.1) + 0.468*T.^5.6.*double(1.1<=T).*double(T<=2.2);
S = @(T) integral(@(Tprime) C_v4(Tprime)./Tprime,0,T);
Then you might have to plug the piece-wise parts into a function and select what integrations you need. Perhaps something like this:
function S4 = S_4_piecewise(Tin)
if Tin > 1.1
S4 = integral(@(T) 0.0516*T.^2,0,0.6) + ...
integral(@(T) .432*T.^4.7,0.6,1.1) + ...
integral(@(T) 0.468*T.^4.6,1.1,Tin);
elseif Tin > 0.6
S4 = integral(@(T) 0.0516*T.^2,0,0.6) + ...
integral(@(T) .432*T.^5.7,0.6,Tin);
else
S4 = integral(@(T) 0.0516*T.^2,0,Tin);
end
HTH
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Bjorn Gustavsson
2021년 3월 22일
Well, then you either put the contents of my function S_4_piecewise inside a loop such that integral can use it, or you do it by hand. And by doing it by hand I mean do it properly, such that you can implement the result in a matlab-function where you also send in parameters for the coefficients and the temperature limits.
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