6.B-01 Definite integrals

Definite integrals

This integration bridge supplies the polynomial calculations used by function-space inner products. Practice emphasizes signed area, endpoint evaluation, products, squared functions and the role of continuity in positive integral norms.

What you will practise

• Evaluate elementary definite polynomial integrals.
• Use linearity and reversed limits.
• Distinguish signed area from integral of a square.
• Normalize a constant using an integral norm.

Begin with recognition and interpretation, then work through calculations, error diagnosis and more demanding reasoning. Single-select and multi-select questions ask you to evaluate the stated assumptions as well as the result. Worked explanations connect the answer to a method or a counterexample, so you can check why tempting alternatives fail.

Before you start

Review polynomial algebra and elementary antiderivatives. Keep a written calculation or short justification for each response, especially when several statements can be correct. This microlearning supports inner products and projections of continuous functions within Module 6 of the Complete Linear Algebra Course.