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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.
This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 2.3, as of 2016-02-29.
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