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• Section 5.2 – The Definite Integral
  • Read pp. 378 – 388
  • online resources:
    1. Riemann Sum Applet - http://www.calvin.edu/~rpruim/courses/m161/F01/java/RiemannSums.shtml
       This site provides a java applet that calculates the left, right, midpoint or trapezoid sums for a user defined function.
    2. Computing Riemann Sums - http://www.calvin.edu/~rpruim/courses/m161/F01/java/RiemannSums.shtml
       This site provides a java applet that calculates the left, right or midpoint sums for a user defined function.
    3. JavaInt - http://www.alpacacriations.com/Nivek/javaint.html
       This site provides a java applet that calculates the left, right, trapezoid or simpson's sums for pre-defined functions.
    4. Definite Integral of a Function - http://mss.math.vanderbilt.edu/~pscrooke/MSS/definiteintegral.html
       This site provides a calculator which computes the definite integral of the user defined function on a given interval.
       
       
• Section 5.3 – The Fundamental Theorem of Calculus (FTC)
  • Note: this section is not part of the syllabus. Here is a good reference for FTC
  • online resources:
    1. The Fundamental Theorem of Calculus - http://ugrad.math.ubc.ca/coursedoc/math101/notes/integration/ftc.html
       This site provides a detailed discussion on FTC and java applets that demonstrates the FTC.
    2. First Form of the Fundamental Theorem of Calculus - http://mss.math.vanderbilt.edu/~pscrooke/MSS/FTC1.html
       This site provides a java applet that calculates the derivative using the FTC.
    3. Cumulative area - http://math.furman.edu/~dcs/java/ftc.html
       This site provides a java applet which demonstrates the FTC.
       
       
• Section 5.5 – The Substitution Rule
  • Read pp. 410 – 416
  • online resources:
    1. Change of variable - http://math.furman.edu/~dcs/java/change.html
       This site provides a java applet which demonstrates the substitution rule.
    2. The Technique of Substitution for Definite Integrals - http://mcis.jsu.edu/faculty/leathrum/Mathlets/subst/
       This site provides a java applet which explores visual aspects of the technique of substitution for finding definite integrals, viewing the substitution as a change of variables.
    3. Integration by Simple Subsitution - http://www.karlscalculus.org/calc11_2.html
       This site provides an interesting discussion of the substitution rule.
       
       

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