improper integral

The definite integral of \( f(x) \) from \( a \) to \( b \) represents the signed area between the graph of \( f(x) \), the x-axis, and the lines \( x = a \) and \( x = b \) and is given by:

\[
\int_{a}^{b} f(x) \, dx
\]

Improper integrals are integrals in which either the interval of integration is unbounded, or the integrand becomes unbounded at one or more points, or both.

Convergence tests for improper integrals are criteria used to determine whether an improper integral converges or diverges without necessarily evaluating the integral explicitly.