Integration (Q8 A2 P2 Edexcel 2022)

In this video, Lee Guffick works through a clean but surprisingly subtle integration question from Edexcel A2 Paper 2 (2022).
The problem involves finding the exact area between a curve and the x-axis, requiring students to identify the correct limits, expand and simplify a rational expression, integrate using Year 12 techniques, and apply the crucial sign change that so many students forget when the area lies below the axis.

Lee demonstrates how to break the algebra down step-by-step, rewriting the function into a sum of simple powers of x, integrating term-by-term, and evaluating the definite integral carefully to reach the required form a multiplied by root 2 add b.

This is a classic A-Level style area question — ideal practice for students strengthening their integration skills and accuracy.

⏱️ TIMESTAMPS:
00:00 Introduction
00:03 Understanding the curve and the region R
00:30 Finding limits by solving where y = 0
01:10 Expanding and simplifying the rational expression
01:40 Splitting into separate integrable terms
02:20 Rewriting using powers of x (Year 12 method)
03:00 Integrating term by term
04:00 Substituting limits at 4 and 2
04:40 Identifying the sign error from area below the axis
05:20 Forming the required answer a multiplied by root 2 add b
06:00 Final explanation and exam tips

✏️ TOPICS COVERED:

Integration of rational functions

Expanding numerators and simplifying algebra

Using powers of x to integrate efficiently

Definite integrals with upper and lower limits

Area under curves below the x-axis

Writing exact answers in the form a multiplied by root 2 add b

💯 EXAM TIPS:

When a curve crosses the x-axis, set the numerator equal to 0 to find the limits.

Simplify the algebra before integrating — it makes the integral far easier.

Always rewrite roots using fractional indices before integrating.

If the region lies below the x-axis, the integral gives a negative value — flip the sign to get the actual area.

Exact values often involve powers like x raised to five over two — evaluate these carefully.

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Lee Guffick is a former Head of Mathematics and A-Level Examiner helping students achieve A star and A grades and secure places at top universities including Oxford, Cambridge and the Ivy League.

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