title: How to use MATLAB to numerically solve equation with unknown embedded in integral?
body: <p>I've been trying to use MATLAB to solve equations like this:</p>
  
  <blockquote>
    <p>B = alpha*Y0*sqrt(epsilon)/(pi*ln(b/a)*sqrt(epsilon_t))*integral from
    0 to pi of
    (2*sinint(k0*sqrt(epsilon*(a^2+b^2-2abcos(theta))-sinint(2*k0*sqrt(epsilon)*a*sin(theta/2))-sinint(2*k0*sqrt(epsilon)*b*sin(theta/2)))
    with regard to theta</p>
  </blockquote>
  
  <p>Where <em>epsilon</em> is the unknown.</p>
  
  <p>I know how to symbolically solve equations with unknown embedded in an integral by using <code>int()</code> and <code>solve()</code>, but using the symbolic integrator <code>int()</code> takes too long for equations this complicated. When I try to use <code>quad()</code>, <code>quadl()</code> and <code>quadgk()</code>, I have trouble dealing with how the unknown is embedded in the integral.</p>