i got some issues trying to integrate a function symbolically

I'm trying to symbolically integrate this function, but it's not working:

>> syms x y s
>> fun = y/((x-s)^2+y^2);
>> int(fun,s,-l/2,l/2)
 
ans =
 
int(y/((s - x)^2 + y^2), s, -l/2, l/2)

why does matlab return me an expression the same as what I typed????? I want an integral in symbolic form instead. The function is to be integrated with respect to variable s only from -l/2 to +l/2 (lower case L)

Answer 1

[Ameer Hamza]

For a general case, the solution might not be expressed in an analytical form. But if x and y are assumed to be real, then you can get an expression

syms x y s l
assume([x y], 'real')
fun = y/((x-s)^2+y^2);
I = int(fun,s,-l/2,l/2)

Result

>> I
I =
atan((l - 2*x)/(2*y)) + atan((l + 2*x)/(2*y))

[Randy Chen]

thank you!

[Randy Chen]

by the way, if I want to plot a contour plot of this function atan((l - 2*x)/(2*y)) + atan((l + 2*x)/(2*y)), how should I do it? I made a meshgrid of x,y and here's what I did:

>> [x,y] = meshgrid(-1:0.1:1,-1:0.1:1);
>> l = 1;
>> contour(c)
Error using contour (line 46)
Input arguments must be numeric or objects which can be converted to double.

i set c = atan((l - 2*x)/(2*y)) + atan((l + 2*x)/(2*y))

[Ameer Hamza]

Following shows one way to do this

syms x y s l
assume([x y], 'real')
fun = y/((x-s)^2+y^2);
I = int(fun,s,-l/2,l/2);

Ifun = matlabFunction(I, 'Vars', {'x', 'y', 'l'});
[xg,yg] = meshgrid(-1:0.01:1);
lv = 1;
Iv = Ifun(xg, yg, lv);
contour(Iv)

[Randy Chen]

thank you!

[Ameer Hamza]

I am glad to be of help!