For questions about definite integrals $\int_a^b f(x),dx$ where the integrand is oscillating, often of the form $f(x) =g(x) e^{i h(x)}$.
An integral is often said to be oscillatory if the integrand fluctuates repeatedly; a precise definition can be given as the limit of the difference between the limsup and liminf of a function. Often these integrals are of the form $\int_a^b g(x) e^{i h(x)}\,dx$, where $g(x)$ is 'well-behaved'.
Questions with this tag often refer to convergence properties of the integral in question and should be used in conjunction with convergence-divergence and integration. A useful technique is a continuous analog of Dirichlet's Theorem: if there is a constant $M$ independent of $y$ such that $\left|\int_a^y B(x)\,dx\right | \le M$ for all $y$ and $A(x)$ is positive, monotonic, and decreasing to zero, then $\int_a^{\infty} A(x)B(x)\,dx$ converges.
