### Integrals - Theory

- Introduction,
namely the definition of a definite and indefinite integral and its
interpretation, basic properties, the connection between the two kinds of
integral etc.
- Methods of integration:
algebraic tricks, substitution, integration by parts, partial fractions. For
the practical approach to integration see
Methods survey.
- Improper integrals: what
is it, how to calculate them, convergence tests.
- Applications (area of
a planar region, curve length, volume of a solid of rotation, etc.).