Integral Lab
Limits, antiderivatives and area under a curve, shown on real graphs.
Integral Lab begins where integral calculus begins, with limits. Students read a limit from a table, a graph or a number line, including one-sided limits, then find limits by direct substitution, factoring, conjugates and limits at infinity. Continuity follows, with types of discontinuity and the constant that makes a piecewise function continuous.
The middle levels move to antiderivatives of powers, sine, cosine and e to the x, with initial values. Then rectangles come in: left, right and midpoint sums, and over and under estimates, drawn at the real function values. The game closes with the Fundamental Theorem, u-substitution with clean answers and set-ups for the area between two curves.
What children practice
- Read limits, including one-sided limits, from tables, graphs and number lines
- Find limits by substitution, factoring, conjugates and at infinity
- Name discontinuities and choose a constant that makes a function continuous
- Find antiderivatives and use an initial value
- Estimate area with left, right and midpoint Riemann sums
- Evaluate definite integrals, use u-substitution and set up area between curves
Levels
- Level 1: Limits from tables and graphs
- Level 2: Algebraic limits
- Level 3: Continuity
- Level 4: Antiderivatives
- Level 5: Riemann sums
- Level 6: The Fundamental Theorem
- Level 7: Substitution and area
- Level 8: Course mix
How it works
- Eight levels move from limits to substitution and area, and Level 8 mixes them all.
- Rectangles sit at the real function values, and shaded regions follow the real curves.
- To unlock a level, your child gives five correct answers and lets the practice timer run its course.
- Antiderivatives always end with plus C unless the question is about a definite integral, and the written forms stay the same across the game.
Best for: A good fit for grades 11 to 12 in a first calculus course, once derivatives are familiar and integrals and limits need more practice.
Tip for parents: Ask your child to estimate the distance a car travels from a few speed readings by multiplying speed by time for each short interval. That is a Riemann sum in everyday clothes.
Questions parents ask
Does the game cover derivatives?
Not as a topic. The derivative of an integral appears as part of the Fundamental Theorem, but differentiation rules have their own game, Derivative Lab.
How are Riemann sums shown?
Level 5 draws rectangles on a graph or reads heights from a table with a few equal strips. A left sum uses the left end of each strip, a right sum the right end, and a midpoint sum the middle.
Can students practice limits alone?
Yes. Levels 1 to 3 are all about limits and continuity, and a student can return to any level already unlocked to play it again.
Ready to try it?
Integral Lab is free with a parent account. A parent adds a child profile, and the child's progress is saved.