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Integration Strategy Decision Flowchart

Run the Integration Strategy Flowchart Fullscreen

About This MicroSim

Facing a new integral can feel overwhelming -- there are so many techniques, and picking the wrong one wastes precious time. This interactive decision flowchart turns technique selection from a guessing game into a systematic process. Start at the top and answer each question about the integrand to arrive at the right strategy.

The flowchart is color-coded by technique family:

  • Green -- Basic antiderivative rules (power rule, trig, exponential)
  • Blue -- Substitution-based techniques (u-substitution, completing the square)
  • Orange -- Algebraic manipulation (simplify first, long division, partial fractions)
  • Yellow diamonds -- Decision points

How to Use

  1. Hover over any node to see an explanation in the side panel
  2. Click an action node (colored rectangle) to see a worked example and highlight the path from start to that technique
  3. Mini-Quiz button launches a 5-question quiz -- given an integral, click the correct technique node
  4. Reset clears highlighting and returns to the default view

Decision Nodes

# Question If Yes
1 Is it a basic antiderivative form? Apply the matching rule directly
2 Can you simplify algebraically? Rewrite first, then integrate
3 Do you see a function and its derivative? u-substitution
4 Is it a rational function P(x)/Q(x)? Long division or partial fractions
5 Is there a quadratic expression inside? Complete the square

If none of the above apply, consider techniques from later chapters (integration by parts, trig substitution) or numerical methods.

Lesson Plan

Learning Objectives

After using this MicroSim, students will be able to:

  1. Evaluate the structure of an integrand to determine the best integration technique (Bloom Level 5)
  2. Select the appropriate method from the available techniques
  3. Judge whether an integral requires algebraic simplification before applying a rule

Suggested Activities

Introduction (5 min)

  • Display the flowchart and walk through the five decision questions
  • Emphasize that the order matters: always check the simplest options first

Guided Practice (10 min)

  • Click through each action node to show the worked examples
  • Discuss how each example matches the decision criteria
  • Point out the path highlighting to reinforce the decision sequence

Independent Practice (10 min)

  • Have students take the Mini-Quiz
  • For each question, students should trace the path on the flowchart before clicking their answer
  • Discuss any questions that students found tricky

Extension

  • Give students a worksheet of 10 integrals and have them classify each one using the flowchart before attempting to solve
  • Students create their own quiz questions for classmates

Common Misconceptions

  • Jumping straight to u-substitution without first checking if the integral is a basic form
  • Forgetting to check if algebraic simplification (splitting fractions, expanding) makes the problem trivial
  • Attempting partial fractions when the degree of the numerator is greater than or equal to the denominator (long division first!)

Embed This MicroSim

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<iframe src="https://dmccreary.github.io/calculus/sims/integration-strategy/main.html" height="520px" width="100%" scrolling="no"></iframe>

References