Add Supplied Rectangle Contributions
A rectangle sum multiplies each supplied height by its interval width and adds the contributions.
About 25 minutes, plus any extended practice
Open lesson 1Introductory Calculus: Integrals and Accumulation
Integration connects signed accumulation with limiting sums. Rectangle models approximate that accumulation, antiderivatives evaluate suitable definite integrals, and the Fundamental Theorem links an accumulation function’s derivative to its continuous integrand.
Before you begin
- Compute rectangle area; differentiate simple polynomials; understand interval endpoints and signed outputs.
Choose by skill rather than age alone. Read with an adult when useful, revisit a lesson, or explore another grade.
Follow the lesson sequence
Evaluate an Antiderivative at Both Bounds
For a continuous integrand, a suitable antiderivative can evaluate a definite integral by subtracting its lower-bound value from its upper-bound value.
About 25 minutes, plus any extended practice
Open lesson 2Separate Net Accumulation from Total Geometric Area
A definite integral counts above-axis regions positively and below-axis regions negatively.
About 25 minutes, plus any extended practice
Open lesson 3Differentiate an Accumulation Function
If a continuous function is accumulated from a fixed lower bound to variable upper input x, the derivative of that accumulation equals the integrand evaluated at x.
About 25 minutes, plus any extended practice
Open lesson 4Review and transfer
After the lessons, try 4 new review cases and a practical task. Each answer has an explanation and a link back to the related lesson.
Open the unit reviewGuest answers are temporary. Keep your own paper or document; this unit does not certify completion or record a school grade.
Topic references
- OpenStax mathematical topic reference: topic reference — Introductory Calculus: Integrals and Accumulation
These references informed the topic selection. They do not certify complete standards alignment.