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A Level Calculus
Trapezium Rule
Learn trapezium rule 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 trapezium rule meaning confidently.
Use trapezium rule representations confidently.
Use trapezium rule methods confidently.
Use trapezium rule applications confidently.
Success checklist
✓I can explain what trapezium rule 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.