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

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

Answer 1

[KSSV]

%% 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))

[Juan David Parra Quintero]

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));

Answer 2

[Walter Roberson]

https://www.mathworks.com/help/matlab/ref/polyint.html

polyint() the component vector to get the integral of the polynomial, and polyval to evaluate.

[Walter Roberson]

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