Integration
A-level Maths (9MA0) · exam-style practice, examiner-report intelligence and the tools that drill it.
The topic on one screen
- Rewrite BEFORE you integrate: every term in the form axn first — split fractions, expand brackets, convert roots to indices.
- Raise the power, divide by the new power, + c. Losing the + c on an indefinite integral is a free mark thrown away.
- Definite integrals: substitute both limits into the integrated expression — show the substitution line, not just the answer.
- The trapezium rule: h/2 x [first + last + 2(middle values)], where h is the strip width. Count strips, not table columns.
- Integration by substitution: change x, dx AND the limits — a definite integral in u needs u-limits.
- Area between curve and line: (top - bottom) integrated between intersection points — find the intersections first.
Where students actually lose marks
The first method mark on indices questions is for expressing the integrand as a sum of terms with indices — students who try to integrate a quotient term-by-term without rewriting score nothing until the rewrite appears.
June 2023 Paper 1 mark scheme (Q01)
Final answers must have indices processed and coefficients exact — an unsimplified power or a rounded coefficient loses the accuracy mark even when the method is right.
June 2023 Paper 1 mark scheme (Q01)
The scheme condones a missing dx mid-working — but a 'spurious integral symbol remaining after integration' is penalised. Close the integral when you integrate.
June 2024 Paper 1 mark scheme (modelling question)
Try it — exam-style
Find ∫ (2x + 5)/√x dx, writing each term in simplest form.
Using the table below and the trapezium rule with 4 strips, estimate ∫ y dx from x = 1 to x = 2. x: 1, 1.25, 1.5, 1.75, 2 · y: 3, 3.6, 4.1, 4.3, 4.2
Evaluate ∫ (3x2 - 4x) dx between x = 1 and x = 3.
Use the substitution u = 2x - 1 to find ∫ x(2x - 1)3 dx.
Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.
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Stuck on integration?
Most integration marks are lost before the integration — in the rewrite. I train that habit until it's automatic, and your first lesson is free.