HAPPY NEW YEAR

– a few more days off and then back to school!

If you haven’t already, it is time to start integration. The posts on starting integration were listed in December since I try to stay ahead of things so you’ll have time to prepare. With that in mind here are past posts on applications of integration – area, volume, average value, improper integrals, accumulation, and some enrichment for BC classes on parametric equations. This will take AB courses well into February. The February postings will be for the BC topics on sequences and series.

The four featured post below are the most popular from this list.

Applications of integration: area, volume, average value of a function, Accumulation and functions defined by integrals.

January 2, 2013 Integration by Parts – 1

January 4, 2013 Integration by Parts – 2

January 7, 2013 Area Between Curves

 A series on visualizing solid figures:

• November 13, 2014 Visualizing Solid Figures 1 Physical models of solid figures
• November 16, 2014 Visualizing Solid Figures 2 Solids with regular cross sections
• November 19, 2014 Visualizing Solid Figures 3 Volume by “Washers”
• November 22, 2014 Visualizing Solid Figure 4 Volume by “Shells”
• November  25, 2014 Visualizing Solid Figures 5  Volume by “Shells” and “Washers” compared

January 9, 2013 Volume of Solids with Regular Cross-sections

January 11, 2013 Volumes of Revolution

January 14, 2013 Why You Never Need Cylindrical Shells

January 25, 2014 Improper Integrals and proper areas.

January 16, 2013 Average Value of a Function

February 6, 2013: Logarithms

January 19, 2013 Most Triangles are Obtuse! What is the probability that a triangle picked at random will be acute? An average value problem solved by a tenth grader.

 A series on ROULETTES some special parametric curves (BC topic – enrichment):

• Rolling Circles
• Epicycloids
• Epitrochoids
• Hypocycloids and Hypotrochoids
• Roulettes and Calculus
• Roulettes and Art – 1
• Roulettes and Art – 2
• Limaçons

Accumulation – On the exams; not in many textbooks 

• January 21, 2103 Accumulation: Need an Amount? Accumulation 1: If you need an amount, look around for a rate to integrate.
• January 23, 2013 AP Accumulation Questions Accumulation 2: AP Exam Rate/Accumulation Questions
• January 26, 2013 Graphing with Accumulation 1 Accumulation 3: Graphing Ideas in Accumulation – Increasing and decreasing
• January 28, 2013 Graphing with Accumulation: Accumulation 4: Graphing Ideas in Accumulation – Concavity
• January 30, 2013 Stamp Out Slope-intercept Form! Accumulation 5: Lines
• February 2, 2014 Accumulation and Differential Equations Accumulation 6: Differential equations
• February 4, 2014 Painting a Point Accumulation 7: An application (of paint)

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