The Definite Integral

 

Definite Integral Thought Exercise

Riemann Sums
Definite Integrals
The Fundamental Theorem of the Calculus
Living Backwards...the Fundamental Theorem
 Chapter 5 Study Guide (MS Word)

Chapter 5 Test (MS Word)

Download Riemann Sum Program (TI-83)
Requires Graph-Link Software

Download Calculus Tools Flash Application (Includes a Riemann Sum Function (TI-89)
Requires Graph-Link Software


 
AP Calculus (BC) Topics
III. Integrals. 
     A.  Riemann sums.  Concept of Riemann sum over equal subdivisions.  Computation of Riemann sums using left, right, and midpoint evaluation points.

     B.  Interpretations and Properties of definite integrals.  Definite integral as a limit of Riemann sums.  Definite integral of the rate of change over an interval interpreted as the change of the quantity over the interval.  Basic properties of definite integrals.  (For example, additivity and linearity.

     G.  Numerical approximation of definite integrals.  Use of Riemann sums and the Trapezoidal Rule to approximate definite integrals of functions represented algebraically, geometrically, and by tables of values.
 
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