Week 11 Study Guide — Integration

Directly supported by notes

The three workshop PDFs cover, in order:

Source	What it covers
Integration rule sheet	Short list of antiderivatives used repeatedly
Indefinite integration exercises	Power rule, $\frac{1}{x}$, exponentials, expansion, mixed sums, and finding $f(x)$ from $f^{\prime }(x)$
Definite integration exercises	Evaluation, find-the-constant problems, and area under a curve

Strongly inferred from workshop materials

The lecture almost certainly covers, in this order:

• The antiderivative concept ($F^{\prime }(x)=f(x)\Rightarrow F(x)+c$).
• Each standard rule with a tiny worked example.
• The chain rule’s reversal — the $\frac{1}{a}$ for $(ax+b)$ forms.
• The Fundamental Theorem of Calculus (${\int }_a^{b}fdx=F(b)-F(a)$).
• Definite integral as signed area; what to do when the curve crosses the x-axis.

Possible lecture content (not in notes)

• $u$-substitution as a method. The workshop exercises don’t require it.
• Integration by parts.
• Improper integrals.

Gaps requiring official source check

• The lecture PDF (EGD105 - Lecture Week 10 - post.pdf — named “Week 10” but covering integration) did not parse cleanly here. Confirm: does the lecture introduce $u$-substitution or integration by parts? The workshop exercises don’t require either.
• The Integration Rules PDF prints $\int kdx=k+c$. This is a typo. The correct rule is $\int kdx=kx+c$. Verify in your own copy.

Worked examples

Two notes cover the topic at different depths:

• Cheatsheet — the full integration rules table, the procedures, quick worked examples, and the quiz.
• In-depth analysis — the two definitions of “integral” connected by the Fundamental Theorem, the chain-rule reasoning behind the $\frac{1}{a}$ factor, signed-vs-geometric area worked out, plus an exam-style end-to-end example.

Common mistakes

Mistake	Fix
Using the power rule on $x^{-1}$	Use $\ln |x|$; the power rule would divide by zero
Forgetting $+c$ on indefinite integrals	Add $+c$ as soon as the antiderivative is written
Dropping the $\frac{1}{a}$ on $e^{ax+b}$, $\sin (ax+b)$, or $(ax+b{)}^n$	Divide by the coefficient of $x$ in the inner linear function
Treating signed integral and geometric area as the same thing	Sketch first, split at roots, then take absolute values for geometric area

Practice questions

Recommended starter set from the workshop PDFs:

• Integration Exercises: 1a, 1d, 1e, 2a, 4a, 7h.
• Definite Integration: 1a, 1c, 1e, 4, 5.

Assessment relevance

Integration appears on every EGD105 exam. Definite integrals applied to area are an extremely common pattern.

Source files used

• school-stuff/EGD105-Calculus/Week11/Integration Rules.pdf
• school-stuff/EGD105-Calculus/Week11/Integration Exercises.pdf
• school-stuff/EGD105-Calculus/Week11/Definite Integration Exercises.pdf