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A Level Calculus
Integration
Learn integration as part of use differentiation, integration, numerical methods and differential equations to analyse change.
Key idea
Connect the algebraic rule to the meaning: differentiation gives gradients and integration accumulates area.
What you will learn
Use integration meaning confidently.
Use integration representations confidently.
Use integration methods confidently.
Use integration applications confidently.
Success checklist
✓I can explain what integration means.
✓I can choose a suitable method without being told.
✓I can show clear working and check my answer.
Worked example
Differentiate 𝑦 = 3𝑥² + 2𝑥.
Step 1
Differentiate 3𝑥² to get 6𝑥.
Step 2
Differentiate 2𝑥 to get 2.
Step 3
dydx = 6𝑥 + 2.
Answer
dydx = 6𝑥 + 2
Quick practice
Question 1
Differentiate 𝑦 = 𝑥² + 4𝑥.
Question 2
Find the gradient of 𝑦 = 𝑥² 𝑎𝑡 𝑥 = 3.
Question 3
Integrate 6𝑥 with respect to 𝑥.
Related resources
These are linked to the wider Calculus topic for now.