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Accumulation Function Explorer

Run the Accumulation Function Explorer Fullscreen

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About This MicroSim

This dual-panel visualization shows the relationship between an integrand f(t) and its accumulation function F(x):

  • Top Panel: Shows f(t) with the shaded region from a to x
  • Bottom Panel: Traces out F(x) as x moves

The key insight: F(x) accumulates the signed area under f(t) from the starting point a to the current position x.

Iframe Code

1
<iframe src="https://dmccreary.github.io/calculus/sims/accumulation-function/main.html" height="552px" scrolling="no" style="width: 100%;"></iframe>

Lesson Plan

Learning Objectives

Students will be able to:

  1. Interpret accumulation functions graphically
  2. Explain how F(x) increases when f(x) > 0 and decreases when f(x) < 0
  3. Connect the rate of accumulation to the value of the integrand

Activities

  1. Drag and Observe (5 min): Move x across the interval and watch F(x) build up
  2. Rate Analysis (10 min): Where is F(x) increasing fastest? How does this relate to f(x)?
  3. Animation Mode (5 min): Watch the automatic animation and predict F(x) behavior

Key Insights

  • When f(x) > 0, F(x) is increasing (accumulating positive area)
  • When f(x) < 0, F(x) is decreasing (accumulating negative area)
  • The slope of F(x) at any point equals f(x) at that point - this is FTC Part 1!

References