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, Simpsonís 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.