Week 11 — Integration

What this week is about

You’re switching from “find the derivative” to “undo the derivative.” Three things to keep separate:

1. Integration rules — the small set of formulas you build everything else from.
2. Indefinite integrals — antiderivatives, with a $+c$.
3. Definite integrals — evaluate between two limits, get a number (often an area).

All three are connected by the Fundamental Theorem of Calculus:

$${\int }_a^{b}f(x)dx=F(b)-F(a)$$

See the in-depth note for what that actually means.

Notes in this week

• Cheatsheet — the full integration rules table, the procedures, common worked examples, and the quiz (mixed difficulty, reshuffles every visit).
• In-depth analysis — both definitions of “integral” reconciled by the FTC, why the $\frac{1}{a}$ appears on $(ax+b)$ forms, signed area vs. geometric area, and full end-to-end worked examples.

Any notes you add to this folder will appear here automatically.

What I need to know before the workshop

• All the standard derivatives — integration is just the reverse.
• The integration rule sheet (it’s small — keep it open while you practise).
• How to handle simple $(ax+b)$ inner functions — divide by $a$.
• The Fundamental Theorem: ${\int }_a^{b}f(x)dx=F(b)-F(a)$.

Assessment relevance

Integration shows up on every exam. Workshop-style “evaluate this integral” questions are direct marks if you know the rules. Definite integral as area is a common applied question.