Answer
$$\int_a^\infty {f\left( x \right)} dx = \mathop {\lim }\limits_{b \to \infty } \int_a^b {f\left( x \right)} dx$$
Work Step by Step
$$\eqalign{
& {\text{To evaluate }}\int_a^\infty {f\left( x \right)} dx{\text{ we must rewrite the upper limit as:}} \cr
& \int_a^\infty {f\left( x \right)} dx = \mathop {\lim }\limits_{b \to \infty } \int_a^b {f\left( x \right)} dx,{\text{ then solve the integral and finally}} \cr
& {\text{evaluate the limit when }}b \to \infty . \cr} $$
