How to numerically evaluate an integral that has symbols in it?

I have an integral that cannot be evaluated symbolically. When I try to do it numerically I want to keep some symbols in the result (to have an output like 10*x1+0.5*x3 where x1 and x3 are symbols) because in a further step I want to build a system of two equations that will solve for x1 and x3. How should I do it? Thanks

for i=1:length(A(1,:))

   x3=sym('x3(t)');
   x1=sym('x1(t)');

   x1_diff=diff(diff(x1,t),t);
    r=D_o-thickness;
    fI1=symfun((x3*sqrt(r^2+(z-zG)^2))/(- (3*x3^5)/40 - x3^3/6 - x3 + pi/2+atan(r/(z-zG))),[t z]);
    fI1_diff=diff(diff(fI1,t),t);
    fI1_diff_z=@(z)(fI1_diff);
    % balast maybe need to revisit if integration doesn't work --> add x1
    % and x3 as variables besides z
    fI1_t=@(z) (density2.*A(2,i)*(x1_diff-fI1_diff));
    % steel cyl
    fI1_t2=@(z) (ro_steel.*A(1,i)*(x1_diff-fI1_diff));
    % deck
    fI1_t3=@(z) (ro_steel.*(A(1,i)+A(2,i))*(x1_diff-fI1_diff));
    % added mass
    fI1_t4=@(z)(density.*(A(1,i)+A(2,i))*(x1_diff-fI1_diff));
    % keep x1 and x3 intact
    FI1(1,i)=integral(fI1_t,-hw,hb-hw)+integral(fI1_t2,-hw,hc-hw)+integral(fI1_t3,hc-hw-hd/2,hc-hw+hd/2)+integral(fI1_t4,-hw,0);

[Vlad]

sorry. in the code the symbols that are to kept intact are x1_diff and x3

Answer 1

[Walter Roberson]

You cannot do that. integral() requires purely numeric values to work with.

You will need to convert the integral to an approximation such as by using taylor or series representation.

[Vlad]

I'll try and work it out with a taylor series. Cheers