Unit 5: The Definite Integral

A. Approximating areas

            1. Riemann sums

                        a. Right sums

                        b. Left sums

            2. Trapezoidal rule

B. Definite integrals and antiderivatives

C. The Fundamental Theorem of Calculus (part 1)

            1.  Finding areas

            2.  Average value of a function

D. Integration using u-substitution

E.  Integration involving trigonometric functions.

F. Integration using the natural logarithmic function

G. The Fundamental Theorem of Calculus (part 2)

H. Separable differential equations

            1. Growth and decay

            2. Slope fields

            3. General differential equations