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Mathematics · Grade 11

The Fundamental Theorem of Calculus

Learners connect the two halves of calculus. Building on accumulation functions, they see why the derivative of an accumulated amount is the rate (Fundamental Theorem, part 1), find antiderivatives, evaluate definite integrals exactly with antiderivatives (part 2), and use the net change theorem and average value in context. An optional honors lesson handles variable upper limits with the chain rule.

  • 5 lessons
  • About 155 minutes
  • Fundamental Theorem check: 12 questions
  • Ways to answer: fill in the blanks, choose an answer, match pairs, type a number, place on a number line and put in order
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What learners will discover

  • Explain and apply part 1 of the Fundamental Theorem: the derivative of an accumulation function is the integrand.
  • Find antiderivatives and indefinite integrals of basic functions, using initial conditions to find the constant.
  • Evaluate definite integrals exactly with part 2 of the Fundamental Theorem.
  • Apply the net change theorem, distinguish displacement from total distance, and compute average values.

Lessons

  1. Accumulation functions have derivatives 5 steps3 practiceabout 34 min
  2. Antiderivatives 5 steps3 practiceabout 32 min
  3. Evaluating definite integrals exactly 5 steps3 practiceabout 32 min
  4. Net change and average value 5 steps3 practiceabout 34 min
  5. Going further (honors): variable limits and the chain rule 4 steps2 practiceabout 23 min
  6. Fundamental Theorem check 12 questions at the end

Keep exploring

More 11th grade math

Guide for grown-ups