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Topic summary · Pure advanced (P4)

Integration 1 summary

Integration techniques begin with standard forms and reverse chain-rule recognition.

Files: P4-Integration 1.pdf · P4-Integration 1 answers.pdf · free public downloads · diagrams in the PDFs

Key learning points

  • Recognise an inside derivative for reverse chain rule.
  • Standard forms include trig, exponential and 1x\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(2x+1)^5.

Working

112(2x+1)6+C\frac{1}{12}(2x+1)^6+C

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

Attempt a matching question on the sheet, then check the Answers PDF.\text{Attempt a matching question on the sheet, then check the Answers PDF.}

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 1x\frac{1}{x}.

Working

Attempt a matching question on the sheet, then check the Answers PDF.\text{Attempt a matching question on the sheet, then check the Answers PDF.}

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

Attempt a matching question on the sheet, then check the Answers PDF.\text{Attempt a matching question on the sheet, then check the Answers PDF.}

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

Attempt a matching question on the sheet, then check the Answers PDF.\text{Attempt a matching question on the sheet, then check the Answers PDF.}

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.

Integration 1 summary — worksheet & answers PDF