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FTC Part 2 Step-by-Step Evaluator

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About This MicroSim

This calculator walks through the FTC Part 2 evaluation process:

\[\int_a^b f(x)\,dx = F(b) - F(a)\]

Each step is revealed one at a time, with the graph showing the shaded area that equals the computed value.

Iframe Code

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<iframe src="https://dmccreary.github.io/calculus/sims/ftc-part2-evaluator/main.html" height="552px" scrolling="no" style="width: 100%;"></iframe>

Lesson Plan

Learning Objectives

Students will be able to:

  1. Apply FTC Part 2 to evaluate definite integrals
  2. Follow the standard evaluation procedure: find antiderivative, apply limits, subtract
  3. Use the bracket notation \([F(x)]_a^b\) correctly

Activities

  1. Step-Through Practice (10 min): Work through each problem, predicting each step
  2. Connection to Area (5 min): Observe how the numerical answer matches the shaded area
  3. Speed Drill (5 min): Try to complete problems faster with each iteration

Evaluation Procedure

  1. Write the integral: \(\int_a^b f(x)\,dx\)
  2. Find antiderivative: \(F(x)\)
  3. Apply bracket notation: \([F(x)]_a^b\)
  4. Evaluate: \(F(b) - F(a)\)
  5. Simplify to final answer

References