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FTC Part 1 Calculator

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About This MicroSim

This step-by-step calculator helps students practice FTC Part 1:

\[\frac{d}{dx}\left[\int_a^x f(t)\,dt\right] = f(x)\]

With chain rule:

\[\frac{d}{dx}\left[\int_a^{g(x)} f(t)\,dt\right] = f(g(x)) \cdot g'(x)\]

Iframe Code

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<iframe src="https://dmccreary.github.io/calculus/sims/ftc-part1-calculator/main.html" height="502px" scrolling="no" style="width: 100%;"></iframe>

Lesson Plan

Learning Objectives

Students will be able to:

  1. Apply FTC Part 1 to find derivatives of accumulation functions
  2. Identify when the chain rule is needed (variable upper limit that isn't just x)
  3. Calculate derivatives of integrals without evaluating the integral

Activities

  1. Basic Problems (5 min): Work through problems where the upper limit is simply x
  2. Chain Rule Problems (10 min): Practice problems where upper limit is a function of x
  3. Predict Before Reveal (5 min): Try to solve each problem before clicking "Next Step"

Key Formula

\[\frac{d}{dx}\left[\int_a^{g(x)} f(t)\,dt\right] = f(g(x)) \cdot g'(x)\]

Don't forget to multiply by the derivative of the upper limit!

References