**Basics: **definite
integral,** **geometric interpretation of, fundamental theorem of calculus, indefinite
integral, antiderivative, inverse function, inverse trigonometric
functions, Riemann sum setup and integral setup for area, volume, work,
hydrostatic force

**Elementary Integrals**: power rule for x^n, trig functions sin, cos,
tan, exponential function e^{ax}, logarithmic function
ln x, and inverse of trigonometric functions as antiderivatives.

**Integration Techniques**: Making use of derivatives and
antiderivatives for elementary functions, summation
rule, substitution method

**Application of Definition Integrals**: area between
curves, volumes by washer and shell methods, work of spring, loading/unloading,
total hydrostatic force, center of mass, growth and decay problems, heating and
cooling problem.

**Numerical approximation**: Riemann sums: left, right,
midpoint, trapezoid, Simpson’s rules.

**Inverse Functions: **definition
of, graphs in relation to the functions, definitions of inverse trigonometric
functions, derivatives of, their integral counterparts.

**Partial Review Problems**: All homework, quiz, lecture example problems, and sample exams.