What you need to know
Check yourself against these “I can” statements.
- I can integrate standard functions, including trig and exponential functions
- I can use trig identities and the reverse chain rule to integrate
- I can integrate by substitution, by parts and using partial fractions
- I can use integration to find areas, including between curves
- I can estimate an area with the trapezium rule
- I can solve simple differential equations and use them to model real situations
Practise this topic
12 resourcesIntegration: Choosing the Method
Integrals that look alike but need different methods, side by side: standard result or f(ax + b), recognition or substitution, identity, recognition or parts, partial fractions, f′/f or divide first, then mixed indefinite and…
⚙️ WorksheetIntegration: Spot the Mistake
A student’s worked solution with a mistake a real student would make (or, about 1 in 8 times, no mistake at all): tap the line you think is wrong, or No mistake, then reveal it, the corrected line and why. Nine levels, one for…
🧮 ToolArea Under a Curve Explorer
Rectangles (left, right, midpoint) and trapezia under a curve, with n from 1 to 100, the estimate, the exact integral, the error and a "let n → ∞" animation showing the limit of a sum becoming the integral. Areas above and below…
🧮 ToolDifferential Equations Explorer
Draws the direction field of dy/dx = f(x, y) for examples from the chapter or a typed equation. Click the field to draw the solution curve through that point, show a family of general solutions with a slider, or type a point for…
🧮 ToolFormula Sheet
Make a printable formula sheet: tick the shapes you want (2D area, perimeter and arc length, volume, surface area, and sector, arc and segment in radians), the eight circle theorems with diagrams, the GCSE formulae sheet…
🧮 ToolIntegral Checker
Type an integrand and an answer to see whether the answer differentiates back to it, with both graphs drawn and where they differ marked. Compare two answers that look different (⅓ln|x| and ⅓ln|3x|) to see whether they differ by…
⬢ BlockbustersIntegration: Choosing the Method Blockbusters
Blockbusters with the questions from the Integration: Choosing the Method worksheet: choose its levels for the ordinary hexagons and for the harder ★ ones. Show the answer and the worked solution, or play against the computer…
📋 Unit reviewIntegration: Exam Questions
Exam-style questions on the whole Integration chapter with mark schemes in the examination’s notation (M, A, B, dM, ft, cso and the AO codes). Choose the difficulty (Standard and Hard at exam level, Advanced in the style of the…
🔗 MatchingIntegration: Ordering
Put the steps of eight pieces of integration working in order: deriving integration by parts, a cyclical integral, a definite integral by substitution, separating the variables with a boundary condition, why integration gives the…
⬢ BlockbustersIntegration: Spot the Mistake Blockbusters
Blockbusters with the questions from the Integration: Spot the Mistake worksheet: choose its levels for the ordinary hexagons and for the harder ★ ones. Show the answer and the worked solution, or play against the computer with…
🔗 MatchingIntegration: Which Method?
Sort integrals by the method you would use (standard result, reverse chain rule or substitution, trig identities, partial fractions, integration by parts), with look-alikes chosen to be confused. Two more modes: classify…
🧮 ToolShape Formulas
Animated visual proofs of the area, volume and surface area formulae: drag the bar (or press Play) to turn each shape step by step into one whose area or volume we already know, with a caption for each step and the formula built…
Topics in this unit
- 11.1 Integrating standard functions · 3 resources
- 11.2 Integrating f(ax + b) · 3 resources
- 11.3 Using trigonometric identities · 2 resources
- 11.4 Reverse chain rule · 4 resources
- 11.5 Integration by substitution · 2 resources
- 11.6 Integration by parts · 3 resources
- 11.7 Partial fractions · 3 resources
- 11.8 Finding areas · 4 resources
- 11.9 The trapezium rule · 2 resources
- 11.10 Solving differential equations · 3 resources
- 11.11 Modelling with differential equations · 2 resources
These are the pages for Integration in the A Level Further Maths scheme of work, following Pearson Edexcel A Level Further Mathematics (9FM0). Open this topic in Mr Wells Maths to see it alongside the rest of the course.