Explicit integral not found

Tarang

2013 5 24

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I have a function in 3 variables in "B y t" which I want to integrate wrt 'y' only. I used int function but it is showing Explicit integral cannot be found. I tried numerical integration also giving limits from (0 to b/2) but same error is there. The code is mentioned below

syms B y t;
C_d=0.1;  w=2;  density=1.225; U=3.2;
a=0.005;  b=0.05;  R=10;
c=2*a*((1-(y/b)^2)^0.5);
C1= 0.5*R/(2.32+R);
C2=0.181+(0.722/R);
A0=0.0348;
theta=-B*y*sin(w*t);
thetarate=-B*y*w*cos(w*t);
thetarate2=-B*y*(w^2)*sin(w*t);
thetabar=sin(w*t)*B*b/4;
h=-0.0785*cos(w*t);
h_dash=0.0785*w*sin(w*t);
A=0.049*(sin(2*t))*cos(B*y*sin(2*t))+0.00234*((1-400*(y^2))^0.5)*B*y*cos(2*t)-B*(y*sin(2*t)-0.0125*sin(2*t));
C=(117*B*cos(2*t)*(1 - 400*y^2)^(1/2))/50000 - (49*B*sin(2*t)^2*sin(B*y*sin(2*t)))/1000 - B*sin(2*t) - (117*B*y^2*cos(2*t))/(125*(1 - 400*y^2)^(1/2));
k=(c*w)/(2*U);
F=1-((C1*(k^2))/((k^2)+(C2^2)));
G=-(C1*C2*k)/((k^2)+(C2^2));
w0=U*2*(A0+thetabar)/(2+R);
alphadash=(R/(2+R))*(F*A+((c/2*U)*G*C))-(w0/U);
Cn=2*pi*(alphadash+A0+thetabar);
V=((U*cos(theta)-0.0785*w*sin(w*t)*sin(theta))^2)+(U*(alphadash+theta)-(0.5*c*thetarate))^0.5;
v_dash=(U*C)-(0.25*c*thetarate2);
N_a=0.25*pi*c^2*density*v_dash;
N_c=0.5*density*U*V*Cn*c;
N=N_a+N_c;
J=2*pi*(alphadash+thetabar-(0.25*c*thetarate/U))^2*density*U*V*c/2;
V_x=U*cos(theta)-(h_dash)*sin(theta);
K=-2*pi*A0*(alphadash+thetabar)*density*U*V*c/2;
L=C_d*density*(V_x)^2*c/2;
M=J-K-L;
O=N*cos(theta)+M*sin(theta);  %final function to integrate
P=M*cos(theta)-N*sin(theta);  %final function to integrate
X=int(O);
Y=int(P);

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Walter Roberson 2013-5-24

Please show the content of "O" and "P" . It could well be that they just do not have an explicit integral.

Please show your attempt to do numeric integration. Is the message exactly the same?

Tarang 2013-5-25

编辑：Tarang 2013-5-25

O and P are very big function in y t and B. When I gave the command... int (O, y, 0, b/2) after 3hrs it said explicit integration can't be found.. and wrote.......... int (O, y=0..0.025).

I think the function is non integrable. But then it should have given the numerical integral. Can I just know how can I integrate above using simpson rule? Should I use linspace and loops or is there any other function for this? Thanks

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