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Mathematics · Grade 11

Integral Techniques and Applications

Learners widen their integration toolkit with substitution, then use integrals to measure: areas between curves, volumes of solids built from disks, washers and known cross-sections, and positions recovered from velocity and acceleration. An optional honors lesson introduces integration by parts.

  • 5 lessons
  • About 155 minutes
  • Integral techniques and applications check: 12 questions
  • Ways to answer: choose an answer, match pairs, type a number, put in order, true or false and write a short answer
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What learners will discover

  • Evaluate indefinite and definite integrals by substitution, changing limits when appropriate.
  • Find the area between two curves, setting up integrals with top minus bottom.
  • Find volumes of solids using disks, washers and known cross-sections.
  • Recover velocity and position from acceleration and velocity with initial conditions.

Lessons

  1. Substitution 5 steps3 practiceabout 34 min
  2. Area between curves 5 steps2 practiceabout 32 min
  3. Volumes by slicing 5 steps3 practiceabout 38 min
  4. Motion from acceleration 4 steps2 practiceabout 28 min
  5. Going further (honors): integration by parts 4 steps2 practiceabout 23 min
  6. Integral techniques and applications check 12 questions at the end

Keep exploring

More 11th grade math

Guide for grown-ups