Countable and uncountable sets.
Riemann integral. Integrability of continuous and monotonic functions. Properties of integrable functions. The fundamental theorem of integral calculus. Mean value theorems of integral calculus. Beta and Gamma functions.
Improper integrals and their convergence, Comparison tests, Absolute and conditional convergence, Abel’s and Dirichlet’s tests. Frullani’s integral.
Integral as a function of a parameter. Continuity, derivability and integrability of an integral of a function of a parameter.