How to solve this integration ????

>> c
 
c =
 
(x*cos(x)*sin(x))/(a^2*cos(x)^2 + b^2*sin(x)^2)^2
 
>> pretty(c)
      x cos(x) sin(x)
--------------------------
  2       2    2       2 2
(a  cos(x)  + b  sin(x) )

>> int(c,0,(pi/2))
 
ans =
 
int((x*cos(x)*sin(x))/(a^2*cos(x)^2 + b^2*sin(x)^2)^2, x, 0, pi/2)
 
>> pretty(ans)
 pi
 --
  2
  /
 |        x cos(x) sin(x)
 |  -------------------------- dx
/     2       2    2       2 2
  0 (a  cos(x)  + b  sin(x) )

Answer 1

[Ameer Hamza]

This shows that MATLAB is not able to find a closed-form expression for the integration problem. You can still find the numerical answer by substituting the numeric values of a and b

syms x a b

c = (x*cos(x)*sin(x))/(a^2*cos(x)^2 + b^2*sin(x)^2)^2;
c_int = int(c, x, 0, pi/1);

x = subs(c_int, [a b], [1 2]);

This will give the value of integration at a=1, b=2. Result:

>> x
x =
-pi/12