Answer
a) $\pi$
b) Only finite numbers are allowed.
Work Step by Step
a) $$\int_1^\infty \pi (\dfrac{1}{x})^2 dx= \pi \lim\limits_{a \to \infty} \int_{1}^{a} x^{-2} dx \\=\pi \lim\limits_{a \to \infty}[-x^{-1}]_{1}^{a} \\ \pi \lim\limits_{a \to \infty}[-\dfrac{1}{x}]_{1}^{a} \\ = \pi (0-(-1)) \\=\pi$$
b) From part (a), it can be seen that we cannot take the limit to infinity since only finite numbers are allowed.
