CHAPTER 5 THE DEFINITE INTEGRAL

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1: Fundamentals 2: Limits and Continuity 3: Derivatives 4: Application of Derivatives 5: The Definite Integral 6: Integration Techniques 7: Solids of Revolution 8: AP Calculus AB Review

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DEFINITE INTEGRAL POWER POINT CLICK BOTTOM RIGHT TO EXPAND AND LAUNCH

integral of the week 

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AP Calculus Standards Covered in this Section
APC.5 The student will investigate derivatives presented in graphic, numerical, and analytic
contexts and the relationship between continuity and differentiability. The derivative will
be defined as the limit of the difference quotient and interpreted as an instantaneous rate
of change.
Mathematics Standards of Learning
60
APC.6 The student will investigate the derivative at a point on a curve. This will include
a) finding the slope of a curve at a point, including points at which the tangent is vertical
and points at which there are no tangents;
b) using local linear approximation to find the slope of a tangent line to a curve at the
point;
c) defining instantaneous rate of change as the limit of average rate of change; and
d) approximating rate of change from graphs and tables of values.
APC.7 The student will analyze the derivative of a function as a function in itself. This will
include
a) comparing corresponding characteristics of the graphs of f, f ', and f ";
b) defining the relationship between the increasing and decreasing behavior of f and the
sign of f ';
c) translating verbal descriptions into equations involving derivatives and vice versa;
d) analyzing the geometric consequences of the Mean Value Theorem;
e) defining the relationship between the concavity of f and the sign of f "; and
f) identifying points of inflection as places where concavity changes and finding points
of inflection.