Integration

Edexcel Pure 8

A-level Maths (9MA0) · exam-style practice, examiner-report intelligence and the tools that drill it.

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Edexcel 9MA0 revision notes Edexcel 9MA0 past papers

The topic on one screen

Rewrite BEFORE you integrate: every term in the form $ax^n$ 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: $\dfrac{h}{2}[\text{first} + \text{last} + 2(\text{middle values})]$ , 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

Medium

ORIGINAL · after June 2023 Paper 1 Q01

Find

\int \dfrac{2x + 5}{\sqrt{x}} \, dx

, writing each term in simplest form.

(4)

(Total for Question 1 is 4 marks)

Medium

ORIGINAL · after June 2023 Paper 1 Q05

Using the table below and the trapezium rule with 4 strips, estimate

\int y \, dx

from

x = 1

x = 2

. x: 1, 1.25, 1.5, 1.75, 2 · y: 3, 3.6, 4.1, 4.3, 4.2

(3)

(Total for Question 2 is 3 marks)

Easy

ORIGINAL

Evaluate

\int (3x^2 - 4x) \, dx

between

x = 1

and

x = 3

(3)

(Total for Question 3 is 3 marks)

Hard

ORIGINAL

Use the substitution

u = 2x - 1

to find

\int x(2x - 1)^3 \, dx

(4)

(Total for Question 4 is 4 marks)

Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.

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Drill it properly

Formulae to Memorise

The standard integrals next to their derivative twins.

Differentiation

Integration marks assume the derivative results are automatic.

Maths flashcards

Integration results and method prompts, spaced-repetition drilled.

Stuck on integration?

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