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Lesson Packs · Grade 12 · Mathematics

Integration by Substitution

Students learn to recognise an integrand that contains a composite function multiplied by the derivative of its inner function. They choose a substitution u, rewrite the integral in terms of u, adjust constant factors, and change the limits of definite integrals.

Unit 4 · Lesson 13 · Integration

Preview

Integration by Substitution — Slide 1
  • Integration by Substitution — Slide 4
    Slide 4
  • Integration by Substitution — Slide 8
    Slide 8
  • Integration by Substitution — Slide 16
    Slide 16
  • Integration by Substitution — Slide 17
    Slide 17
  • Integration by Substitution — Worksheet, page 1
    Worksheet, page 1
  • Integration by Substitution — Answer key, page 1
    Answer key, page 1

Learning objectives

  • Choose a substitution u = g(x) when an integrand has the form f(g(x)) · g′(x).
  • Rewrite an integral in terms of u and du, adjust constant factors, and give the answer in terms of x.
  • Evaluate definite integrals by substitution, changing the limits of integration to values of u.

What's inside

  • 39 PowerPoint slides: lesson, worked examples and the worksheet with solutions
  • 11 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).

Do downloads count toward my plan?

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