How to integrate the function in Matlab?
2 views (last 30 days)
Show older comments
given y(t) = a*x+b*(((t^2/2)+t))+c*(((t^3/3)+t^2+t))+d*(((t^4/4)+t^3+((3*t^2)/2)+t))+e*(((t^5/5)+t^4+2*t^3+2*t^2+t))+f*(((t^6/6)+t^5+((5*t^4)/2)+((10*t^3)/3)+((5*t^2)/2)+t))
int((exp(x-t)*(y(t)^3)),t,0,1)
0 Comments
Answers (1)
Ameer Hamza
on 1 May 2020
Edited: Ameer Hamza
on 1 May 2020
Try this
syms t
s = 0.3;
a = 0.2;
b = 0.5;
c = 0.3;
d = 0.8;
e = 0.1;
f = 0.8;
x = 0.3;
y = a*x+b*(((t^2/2)+t))+c*(((t^3/3)+t^2+t))+d*(((t^4/4)+t^3+((3*t^2)/2)+t))+e*(((t^5/5)+t^4+2*t^3+2*t^2+t))+f*(((t^6/6)+t^5+((5*t^4)/2)+((10*t^3)/3)+((5*t^2)/2)+t));
y_int = int((exp(x-t)*(y^3)),t,0,1);
y_int2 = vpa(y_int);
disp(y_int) % symbolic output
disp(y_int2) % output in decimal format
Result
(3*exp(-7/10)*(14312622602045415832*exp(1) - 38905741936622033629))/1000000
164.22632490929883023849072628867
2 Comments
Ameer Hamza
on 1 May 2020
If they are unknown constants, then you can also define them as symbolic variables
syms t s a b c d e f x
y = a*x+b*(((t^2/2)+t))+c*(((t^3/3)+t^2+t))+d*(((t^4/4)+t^3+((3*t^2)/2)+t))+e*(((t^5/5)+t^4+2*t^3+2*t^2+t))+f*(((t^6/6)+t^5+((5*t^4)/2)+((10*t^3)/3)+((5*t^2)/2)+t));
y_int = int((exp(x-t)*(y^3)),t,0,1);
The output will be a symbolic expression in term of (s a b c d e f x).
y_int = 20339574*d^3*exp(x) + 28436783046*e^3*exp(x) + 80571537949566*f^3*exp(x) - (4821*b^3*exp(x - 1))/8 - (2665441*c^3*exp(x - 1))/27 - (3538475895*d^3*exp(x - 1))/64 - (9662398822711*e^3*exp(x - 1))/125 - (1752129179993373*f^3*exp(x - 1))/8 + 222*b^3*exp(x) + 36318*c^3*exp(x) - a^3*x^3*exp(x - 1) + 17838*b*c^2*exp(x) + 3252*b^2*c*exp(x) + 914130*b*d^2*exp(x) + 19818*b^2*d*exp(x) + 77530230*b*e^2*exp(x) + 6773016*c*d^2*exp(x) + 143892*b^2*e*exp(x) + 819570*c^2*d*exp(x) + 9819703674*b*f^2*exp(x) + 676668594*c*e^2*exp(x) + 1205850*b^2*f*exp(x) + 7218954*c^2*e*exp(x) + 98703428940*c*f^2*exp(x) + 7108899858*d*e^2*exp(x) + 72227142*c^2*f*exp(x) + 634676832*d^2*e*exp(x) + 1184848286826*d*f^2*exp(x) + 7404854034*d^2*f*exp(x) + 16114285888956*e*f^2*exp(x) + 1137476253630*e^2*f*exp(x) - (96967*b*c^2*exp(x - 1))/2 - (35345*b^2*c*exp(x - 1))/4 - (79515243*b*d^2*exp(x - 1))/32 - (861849*b^2*d*exp(x - 1))/16 - (10537449387*b*e^2*exp(x - 1))/50 - (294575189*c*d^2*exp(x - 1))/16 - (7822617*b^2*e*exp(x - 1))/20 - (26733731*c^2*d*exp(x - 1))/12 - (213541775907*b*f^2*exp(x - 1))/8 - (45984397557*c*e^2*exp(x - 1))/25 - (26222619*b^2*f*exp(x - 1))/8 - (294347011*c^2*e*exp(x - 1))/15 - (1073214948765*c*f^2*exp(x - 1))/4 - (1932399324261*d*e^2*exp(x - 1))/100 - (1178002201*c^2*f*exp(x - 1))/6 - (138018436773*d^2*e*exp(x - 1))/80 - (51532025078445*d*f^2*exp(x - 1))/16 - (644111363199*d^2*f*exp(x - 1))/32 - (876063410205933*e*f^2*exp(x - 1))/20 - (30919810303923*e^2*f*exp(x - 1))/10 + a^3*x^3*exp(x) - (447*a*b^2*x*exp(x - 1))/4 + 6*a^2*b*x^2*exp(x) - (5221*a*c^2*x*exp(x - 1))/3 + 15*a^2*c*x^2*exp(x) - (892563*a*d^2*x*exp(x - 1))/16 + 48*a^2*d*x^2*exp(x) - (80434323*a*e^2*x*exp(x - 1))/25 + 195*a^2*e*x^2*exp(x) - (1179786123*a*f^2*x*exp(x - 1))/4 + 978*a^2*f*x^2*exp(x) + 242628*b*c*d*exp(x) + 1948164*b*c*e*exp(x) + 17901792*b*c*f*exp(x) + 16125516*b*d*e*exp(x) + 161510964*b*d*f*exp(x) + 130095204*c*d*e*exp(x) + 1681817136*b*e*f*exp(x) + 1409661276*c*d*f*exp(x) + 15791037732*c*e*f*exp(x) + 177725405940*d*e*f*exp(x) - (27*a^2*b*x^2*exp(x - 1))/2 - 37*a^2*c*x^2*exp(x - 1) - (501*a^2*d*x^2*exp(x - 1))/4 - (2613*a^2*e*x^2*exp(x - 1))/5 - (5295*a^2*f*x^2*exp(x - 1))/2 - (2638063*b*c*d*exp(x - 1))/4 - 5295635*b*c*e*exp(x - 1) - (97324157*b*c*f*exp(x - 1))/2 - (876673227*b*d*e*exp(x - 1))/20 - (3512258097*b*d*f*exp(x - 1))/8 - (707270753*c*d*e*exp(x - 1))/2 - (45716528721*b*e*f*exp(x - 1))/10 - (15327426191*c*d*f*exp(x - 1))/4 - (214622453951*c*e*f*exp(x - 1))/5 - (9662154824511*d*e*f*exp(x - 1))/20 + 42*a*b^2*x*exp(x) + 642*a*c^2*x*exp(x) + 20526*a*d^2*x*exp(x) + 1183614*a*e^2*x*exp(x) + 108504786*a*f^2*x*exp(x) - 825*a*b*c*x*exp(x - 1) - (15357*a*b*d*x*exp(x - 1))/4 - (108957*a*b*e*x*exp(x - 1))/5 - (36995*a*c*d*x*exp(x - 1))/2 - (292551*a*b*f*x*exp(x - 1))/2 - (593894*a*c*e*x*exp(x - 1))/5 - 891961*a*c*f*x*exp(x - 1) - (8040531*a*d*e*x*exp(x - 1))/10 - (26807721*a*d*f*x*exp(x - 1))/4 - 58988181*a*e*f*x*exp(x - 1) + 306*a*b*c*x*exp(x) + 1416*a*b*d*x*exp(x) + 8022*a*b*e*x*exp(x) + 6810*a*c*d*x*exp(x) + 53820*a*b*f*x*exp(x) + 43704*a*c*e*x*exp(x) + 328146*a*c*f*x*exp(x) + 295806*a*d*e*x*exp(x) + 2465520*a*d*f*x*exp(x) + 21700566*a*e*f*x*exp(x)
you can use subs() function to substitute specific values of these constants
See Also
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!