7-4

$\displaystyle \Int dx\, f(x)\delta(x^2-1)$	$\displaystyle =\left(\int_{-\infty}^{-1-\epsilon} +\int_{-1-\epsilon}^{-1+\epsi... ...+\int_{1+\epsilon}^{+\infty}\right) dx\, f(x)\delta(x^2-1)\,; \qquad \epsilon>0$
	$\displaystyle =\int_{-1-\epsilon}^{-1+\epsilon} dx\, f(x)\delta(x^2-1)+ \int_{+1-\epsilon}^{+1+\epsilon} dx\, f(x)\delta(x^2-1)$
	$\displaystyle =\int_{\epsilon^2 -2\epsilon}^{\epsilon^2 +2\epsilon} dX\,\frac{f... ...on \\ \hline X & \epsilon^2 +2\epsilon & \to & \epsilon^2-2\epsilon \end{array}$
	$\displaystyle \,\,\,\,\, + \int_{\epsilon^2 -2\epsilon}^{\epsilon^2 +2\epsilon}... ...on \\ \hline X & \epsilon^2 -2\epsilon & \to & \epsilon^2+2\epsilon \end{array}$
	$\displaystyle =\frac{1}{2}\left\{ f(-1)+f(+1)\right\}$