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.
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Title from PDF title page (viewed on December 9, 2015).
