Mathematics · Mission: Oliver's Interactive Math Adventure
Integration
Discover what integration means, why it is useful, how its symbols work, and how its formulas are built from real-life situations.
🎯 By the end, students should be able to explain integration in their own words, distinguish indefinite and definite integration, read a simple integral, and understand the power rule in a real example.
🧑🌾 Your guide: Oliver, a curious student living in the countryside. · Source: Beginners / school students (7-page lesson storyboard)
Levels
0/6
XP
0
Rank
Trainee
Streak
0 days
Mastered
0/15
Final
—
Mission map
- 1Level 1The TankControl a constant tap and watch the water level rise.Unlock condition: explain why multiplication works.
- 🔒Level 2Changing FlowSee different amounts delivered in different time blocks.Pass Level 1 to unlock
- 🔒Level 3Tiny IntervalsSplit time into smaller pieces and improve the estimate.Pass Level 2 to unlock
- 🔒Level 4Integral SignTap each symbol to reveal its meaning.Pass Level 3 to unlock
- 🔒Level 5Formula LabBuild the power rule one step at a time.Pass Level 4 to unlock
- 🔒Level 6Two Types of IntegrationCompare general answers with answers over a specified interval.Pass Level 5 to unlock
Practice & assessment
Guided practice
Questions from levels you've unlocked, with hints.
🎯Independent practice
No hints, plus fresh engine-generated questions. Proves mastery.
🔁Revision practice
Targets your weak concepts and past mistakes.
🗣️Oral revision
Explain ideas out loud to your teacher.
🏁Final assessment
The end-of-course test. 70% to pass.
⚡Challenge mode
Harder mixed questions, no hints. Beat your best.
Badges
Concept mastery
Mastery needs repeated correct answers including at least one without help — finishing a lesson alone doesn’t count.
- Accumulationnot started
- Constant flow: rate × timenot started
- Adding changing contributionsnot started
- Tiny intervalsnot started
- Slice estimates (Riemann-style)not started
- Reading the integral signnot started
- Area under a curvenot started
- Units of an integralnot started
- Differentiation as rate of changenot started
- Integration reverses differentiationnot started
- The constant Cnot started
- Power rulenot started
- Indefinite integrationnot started
- Definite integrationnot started
- Real-world applicationsnot started
Glossary
- Integration
- — A way to add up many tiny contributions to find a total.
- ∫
- — The integral sign: accumulate, add up all the tiny contributions.
- dt
- — A tiny interval of time.
- Limits
- — The starting and ending values of the interval.
- Integrand
- — The expression being integrated — it describes the changing quantity.
- Differentiation
- — Measuring how quickly something changes.
- C
- — An unknown fixed number (constant of integration).
- Indefinite integral
- — A general expression with C and no limits.
- Definite integral
- — Accumulation over specified limits — a number.
Accuracy notes
- Do not show a formula before the real-life problem is clear.
- Keep units visible: litres, minutes, litres per minute, metres, and seconds.
- Do not imply that all changing-rate problems can be solved by one average. The triangle example is exact because its rate changes linearly.
- A definite integral of velocity gives displacement; it equals distance only when movement stays in one direction.
- Source typo: Scene 10's “9/3 = 9/1?” is corrected to ∫₀³ t² dt = 9.
Optional extensions
- Left, right and midpoint slices. The tiny-interval lab can use the rate at the start, end or middle of each slice; for a straight-line rate the midpoint estimate is already exact.
- Any number of slices. Beyond the PDF's 3, 6 and 12, the lab goes up to 120 slices to show the estimate converging to 4.5.