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📘 Integration

The reverse of differentiation: antiderivatives, Riemann sums, the Fundamental Theorem of Calculus, and the integration techniques that turn impossible-looking integrals into one-line answers.

Topics

📋 Introduction (Pretest)

Diagnostic: see what you remember and what needs work.

Coming when we start

↩️ Antiderivatives

Find $F(x)$ given $F'(x) = f(x)$.

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📐 The Area Problem and Riemann Sums

Area as a limit of rectangles.

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🧠 The Definite Integral and the Fundamental Theorem of Calculus

Differentiation and integration are inverses — the big theorem.

Coming when we start

∫ The Indefinite Integral

Antiderivatives as a family of functions — the $+\,C$ story.

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🔄 Substitution

The chain rule in reverse — the workhorse integration technique.

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📊 Area Under a Curve

Areas between a function and the $x$-axis.

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📈 Area Between Curves

Areas between two functions.

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✅ Conclusion (Posttest)

End-of-module assessment.

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