Intermediate calculus : methods of integration

1. Understanding the integration of parts.
Integration by parts for indefinite integrals.
Integration by parts for definite integrals.
Integration by parts for definite integrals.

2. Indefinite integrals and rational functions.
Special cases.
Arbitrary rational functions.

3. Using integrals for trigonometric and hyperbolic functions.
Products of sin(x) and cos(x) or sinh(x) and cosh(x).
Special integrals that involve sin (mx) and cos (nx).
Rational functions of sin(x) and cos(x) or sinh(x) and cosh(x).

4. Integrations using trigonometric and hyberbolic substitutions.
The substitution x = a sin (u).
The substitution x = a sinh (u).
The substitution x = a cosh (u).

5. Approximations in numerical integration.
Riemann sums.
The trapezoid rule.
Simpson's rule.
The derivation of Simpson's rule.

6. Improper integrals: unbounded intervals and discontinuities.
Improper integrals on unbounded intervals.
Improper integrals that involve discontinuous functions.

7. Improper integrals: using convergence tests.
Improper integrals on unbounded intervals.
Improper integrals that involve discontinuous functions.

Index.