Solution
= Solution
The <interfacial tension> is the excess free energy per unit interfacial area:
$$
\sigma=\int_{-\infty}^{\infty}
\left[
f(\phi)-f(\phi_B)
+\frac{\kappa(\phi)}2(\phi')^2
\right]dx.
$$
The first integral from part e equates the first two terms inside the brackets to $\kappa(\phi)(\phi')^2/2$. Hence
$$
\boxed{
\sigma=\int_{-\infty}^{\infty}
\kappa(\phi)(\partial_x\phi)^2\,dx
}.
$$