Integration 1 summary

Key learning points

• Recognise an inside derivative for reverse chain rule.
• Standard forms include trig, exponential and $\frac{1}{x}$.
• Evaluate definite integrals carefully with signs.
• Area setups appear frequently in later exercises.

Worked example 1 — Reverse chain

Integrate $(2x+1)^5$.

Working

Divide by the inside derivative 2 and by 6.

Worked example 2 — Recognise an inside derivative for reverse chain rule

Use this method from the Integration 1 sheet: Recognise an inside derivative for reverse chain rule.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 3 — Standard forms include trig, exponential and

Use this method from the Integration 1 sheet: Standard forms include trig, exponential and $\frac{1}{x}$.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 4 — Evaluate definite integrals carefully with signs

Use this method from the Integration 1 sheet: Evaluate definite integrals carefully with signs.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 5 — Area setups appear frequently in later exercises

Use this method from the Integration 1 sheet: Area setups appear frequently in later exercises.

Working

Each key learning point matches a question type on the printable worksheet.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.