100-level Mathematics Revision Exercises

Integration Methods

These revision exercises will help you practise the procedures involved in integrating functions and solving problems involving applications of integration. Worksheets 1 to 7 are topics that are taught in MATH108. Worksheets 8 to 21 cover material that is taught in MATH109.

  1. Signed area (solutions)
  2. Integration by substitution: Indefinite integrals (solutions)
  3. Integration by substitution: Definite integrals (solutions)
  4. Integration by parts (solutions)
  5. Integration by substitution and parts (solutions)
  6. Reduction formulas (solutions)
  7. Trigonometric integral formulas (solutions)
  8. Integration by trig substitution (solutions)
  9. Integration by substitution: Challenge (solutions)
  10. Introduction to partial fractions (solutions)
  11. Integration using partial fractions: One (solutions)
  12. Integration using partial fractions: Two (solutions)
  13. Integration using partial fractions: Three (solutions)
  14. Improper integrals (solutions)
  15. Integration techniques: Exam questions (solutions)
  16. Arc length (solutions)
  17. Revision: Arc length (solutions)
  18. Revision: Integration by parts (solutions)
  19. Revision: Trig integral formulas (solutions)
  20. Revision: Trig substitutions (solutions)
  21. Revision: Partial fractions (solutions)

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