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Lesson Packs · Grade 12 · Mathematics

Definite Integrals and the Fundamental Theorem of Calculus

Students estimate areas with rectangles, define the definite integral as a limit of Riemann sums and as net signed area, use its properties, and apply both parts of the Fundamental Theorem of Calculus to evaluate and differentiate integrals.

Unit 4 · Lesson 15 · Integration

Preview

Definite Integrals and the Fundamental Theorem of Calculus — Slide 1
  • Definite Integrals and the Fundamental Theorem of Calculus — Slide 4
    Slide 4
  • Definite Integrals and the Fundamental Theorem of Calculus — Slide 10
    Slide 10
  • Definite Integrals and the Fundamental Theorem of Calculus — Slide 17
    Slide 17
  • Definite Integrals and the Fundamental Theorem of Calculus — Slide 18
    Slide 18
  • Definite Integrals and the Fundamental Theorem of Calculus — Worksheet, page 1
    Worksheet, page 1
  • Definite Integrals and the Fundamental Theorem of Calculus — Answer key, page 1
    Answer key, page 1

Learning objectives

  • Estimate the area under a curve with rectangles and interpret ∫ₐᵇ f(x) dx as a net signed area.
  • Use the properties of definite integrals: constant multiples, sums, reversed limits and adjacent intervals.
  • Apply the Fundamental Theorem of Calculus to evaluate definite integrals and to differentiate ∫ₐˣ f(t) dt.

What's inside

  • 43 PowerPoint slides: lesson, worked examples and the worksheet with solutions
  • 12 worksheet questions (34 marks) with step-by-step solutions
  • Printable worksheet (4 pages) and a teacher answer key
  • Fully editable in PowerPoint, Google Slides, Keynote and Word

More lessons in this unit

Questions teachers ask

Can I edit the files?

Yes. The PowerPoint and the Word worksheet are fully editable, so you can change examples, add questions or adapt the design for your class.

How do I use the worksheet slides?

After the teaching slides, each worksheet question appears on its own slide. Let students try it first, then show the next slide and work through the solution together.

Is there an answer key?

Yes. The Word file ends with a teacher answer key that has the answer and a worked solution for every question. It is also included as a separate PDF.

Which languages are available?

Every Lesson Pack is made in 18 languages: English, Simplified Chinese, Hindi, Spanish, Arabic, French, Bengali, Portuguese, Indonesian, Urdu, Vietnamese, Albanian, Italian, German, Turkish, Malay, Greek and Traditional Chinese (Hong Kong).

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