# Improper Integrals

##### 86 words — categories: calculus

An improper integral is an integral that has infinity in one of its “extremities”.

\[\int_a^\infty f(x)dx = \lim_{b \to \infty} \int_a^b f(x)dx\]

This means that the upper limit of this integral is the limit that \(b\) approaches as \(b\) goes to infinity. If the limit exists, we say tha the improper integral **converges**, otherwise, we say that it **diverges**.

Two more type of improper integrals follow from the first definition.

\[\int_{-\infty}^b f(x)dx = \lim_{a \to -\infty} \int_a^b f(x)dx\]

\[\int_{-\infty}^\infty f(x)dx = \int_{-\infty}^c f(x)dx + \int_{c}^{\infty} f(x)dx\]