In this, the fourth section of the course, the topics include:
Interpretations and properties of definite integrals
• Definite integral as a limit of Riemann sums.
• Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval.
• Basic properties of definite integrals (examples include additivity and linearity).
Fundamental Theorem of Calculus
• Use of the Fundamental Theorem to evaluate definite integrals.
• Use of the Fundamental Theorem to represent a particular antiderivative and
the analytical and graphical analysis of functions so defined.
Techniques of antidifferentiation
• Antiderivatives following directly from derivatives of basic functions.
• Antiderivatives by substitution of variables (including change of limits for
Numerical approximations to definite integrals.
• Use of Riemann sums (using left, right, and midpoint evaluation points) and
trapezoidal sums to approximate definite integrals of functions represented
algebraically, graphically, and by tables of values.