explicit integral could not be found for the double integral below

Dear all,

i am trying to solve double integral of the following function but it says

,Warning :explicit integral could not be found

please help

the function is

q = int(int(((6*alpha*xm3*yn*xm*yn)/(a+(alpha*x))),0,1),0,1)

where

xm = sin((pi*x)/a)
xm3 = diff(xm,3)
yn =sin(((pi*y)/b)
alpha =0.1
a= 1
b= 1

please help thank you in advance

prasad joshi

[Walter Roberson]

Is there good reason to expect that it will have a closed form ?

What are your variables of integration? x and y?

[prasad joshi]

yes sir, integration var are x and y. i think reduction integration is used to solve this. but is it available in matlab

[Walter Roberson]

To check: does diff(xm,3) mean diff(diff(diff(xm,x),x),x) ?

If it does then the solution appears to be

-(3/2)*pi^3*(Si(22*pi)-Si(20*pi))

where Si is the "sine integral", int(sin(t)/t, t=0..x)

Answer 1

[Andrei Bobrov]

syms x y alpha a b

xm = sin(pi*x/a);
xm3 = diff(xm,3);
yn =sin(pi*y/b);

fun1 = matlabFunction( 6*alpha*xm3*yn*xm*yn/(a+alpha*x),'vars',[x y alpha a b]);

alpha =0.1;
a= 1;
b= 1;

out = integral2(@(x,y)fun1(x,y,alpha,a,b),0,1,0,1);

variant of the integral

out = dblquad(@(x,y)fun1(x,y,alpha,a,b),0,1,0,1);

[prasad joshi]

Dear Andrei, I tried what u have written, but it is not working. please clarify. error with your solution is : Error in ==> Untitled at 9 out = integral2(@(x,y)fun1(x,y,alpha,a,b),0,1,0,1)

[Andrei Bobrov]

Please give full message about error and give your code.

[Walter Roberson]

prasad, which MATLAB version are you using? integral2() is relatively new.

[Andrei Bobrov]

Try using dblquad.

[prasad joshi]

thank you sir, integral2 is not there in matlab7.12. i tried with dblquad, it works and ans i got is -0.0672. kindly let me know . is the ans correct with dblquad. what does matlabFunction do. regards prasad