Diện tích hình phẳng S(a) là:

\[S\left( a \right) = \int\limits_1^a {\frac{3}{{{x^2}}}} dx\]

        \[ = 3\int\limits_1^a {\frac{1}{{{x^2}}}} dx = \left. {\frac{{ - 3}}{x}} \right|_1^a = 3\left( {1 - \frac{1}{a}} \right).\]

Ta có: \[\mathop {\lim }\limits_{a \to  + \infty } S\left( a \right) = \mathop {\lim }\limits_{a \to  + \infty } 3\left( {1 - \frac{1}{a}} \right) = 3.\]

Vậy \[\mathop {\lim }\limits_{a \to  + \infty } S\left( a \right)\] = 3.