Integrate a polyfit-polyval in matlab, I would appreciate any input. I want to calculate the integral of the sine function from a trend li

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Juan David Parra Quintero
评论： Walter Roberson 2022-8-12
X=[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 ];
Y=[ 0 0.017451121 0.034896927 0.052332105 0.069751344 0.08714934 0.104520792 0.121860412 0.139162917 0.156423038 0.173635518 0.190795114 0.207896601 0.224934771 0.241904433 0.258800419 0.275617584 0.292350805 0.308994987 0.32554506 0.341995983 0.358342746 0.374580371 0.390703911 0.406708457 0.422589134 0.438341105 0.453959573 0.469439781 0.484777014 0.4999666 0.515003915 0.529884377 0.544603456 0.559156667 0.573539579 0.587747811 0.601777035 0.61562298 0.629281427 0.642748218 0.65601925 0.669090481 0.681957931 0.694617681 0.707065874 0.719298721 0.731312494 0.743103535 0.754668253 0.766003125 0.7771047 0.787969596 0.798594504 0.808976189 0.819111488 0.828997314 0.838630657 0.848008582 0.857128234 0.865986835 0.874581687 0.882910172 0.890969753 0.898757976 0.90627247 0.913510945 0.920471196 0.927151104 0.933548635 0.939661839 0.945488856 0.95102791 0.956277314 0.96123547 0.965900868 0.970272086 0.974347793 0.978126748 0.9816078 0.984789889 0.987672046 0.990253392 0.992533143 0.994510602 0.996185169 0.997556332 0.998623675 0.999386873 0.999845692 0.999999993 ];
plot(X,Y)
p2=polyfit(X,Y,4);
p3=polyfit(X,Y,3);
hold on
c=polyval(p2,X);
plot(X,c)
FS=7;
leg = legend(["Seno","Aproximacion Seno"],'Location','northwest','Orientation','horizontal','FontSize',FS,"NumColumns",1);
x1 = 12;
x2 = 12;
leg.ItemTokenSize = [x1, x2];
legend('boxoff');
hold off

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采纳的回答

KSSV
KSSV 2022-8-11
%% Integration
p2=polyfit(X,Y,4);
fun = @(x) p2(1)*x.^4+p2(2)*x.^3+p2(3)*x.^2+p2(4)*x+p2(5) ; % using p2 from polyfit
val = integral(fun,X(1),X(end))
  1 个评论
Juan David Parra Quintero
Juan David Parra Quintero 2022-8-11
Note that the integral must give 1 between 0 and 90 degrees of the sine function, but with the code it gives 57.2. Do you know what error is happening?
X=[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 ];
Y=[ 0 0.017451121 0.034896927 0.052332105 0.069751344 0.08714934 0.104520792 0.121860412 0.139162917 0.156423038 0.173635518 0.190795114 0.207896601 0.224934771 0.241904433 0.258800419 0.275617584 0.292350805 0.308994987 0.32554506 0.341995983 0.358342746 0.374580371 0.390703911 0.406708457 0.422589134 0.438341105 0.453959573 0.469439781 0.484777014 0.4999666 0.515003915 0.529884377 0.544603456 0.559156667 0.573539579 0.587747811 0.601777035 0.61562298 0.629281427 0.642748218 0.65601925 0.669090481 0.681957931 0.694617681 0.707065874 0.719298721 0.731312494 0.743103535 0.754668253 0.766003125 0.7771047 0.787969596 0.798594504 0.808976189 0.819111488 0.828997314 0.838630657 0.848008582 0.857128234 0.865986835 0.874581687 0.882910172 0.890969753 0.898757976 0.90627247 0.913510945 0.920471196 0.927151104 0.933548635 0.939661839 0.945488856 0.95102791 0.956277314 0.96123547 0.965900868 0.970272086 0.974347793 0.978126748 0.9816078 0.984789889 0.987672046 0.990253392 0.992533143 0.994510602 0.996185169 0.997556332 0.998623675 0.999386873 0.999845692 0.999999993 ];
plot(X,Y)
p2=polyfit(X,Y,4);
hold on
time= linspace(0,90,90);
c=polyval(p2,time);
plot(time,c)
FS=7;
leg = legend(["Seno","Aproximacion Seno"],'Location','northwest','Orientation','horizontal','FontSize',FS,"NumColumns",1);
T1 = 12;
T2 = 12;
leg.ItemTokenSize = [T1, T2];
legend('boxoff');
hold off
fun = @(x) p2(1)*x.^4+p2(2)*x.^3+p2(3)*x.^2+p2(4)*x+p2(5) ; % using p2 from polyfit
val = integral(fun,X(1),X(end));

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更多回答（1 个）

Walter Roberson
Walter Roberson 2022-8-11
https://www.mathworks.com/help/matlab/ref/polyint.html
polyint() the component vector to get the integral of the polynomial, and polyval to evaluate.
  1 个评论
Walter Roberson
Walter Roberson 2022-8-12
You are not integrating sin(x), you are integrating sind(x). sind(x) = sin(alpha*x) for alpha = π/180
syms alpha x
int(sin(alpha*x), x, 0, sym(pi)/2/alpha)
ans = 1/alpha
with alpha being π/180, then 1/alpha is 180/π which is 57 point something

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