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Lesson Packs · Grade 12 · Mathematics

Integration by Parts

Students derive the integration by parts formula from the product rule and use the LIATE guideline to choose u. They integrate products of polynomials with exponential, trigonometric and logarithmic functions, integrate ln x, apply the formula twice and evaluate definite integrals.

Unit 4 · Lesson 14 · Integration

Preview

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

Learning objectives

  • Derive the formula ∫ u dv = uv − ∫ v du from the product rule.
  • Integrate xeˣ, x cos x and ln x by parts, choosing u with the LIATE guideline.
  • Apply integration by parts twice when needed, and evaluate definite integrals by parts.

What's inside

  • 37 PowerPoint slides: lesson, worked examples and the worksheet with solutions
  • 10 worksheet questions (32 marks) with step-by-step solutions
  • Printable worksheet (3 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.

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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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