WMA12/01 Jun 2025, Question 3: Definite Integrals and Areas
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 5 marks
The question, in short
Using algebraic integration, determine the area of region R enclosed between the curve y = 3x + 16/x² − 8 and the straight line segment joining P(1, 11) and Q(4, 5).
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Solution · 5 marks
- 1∫ (3x + 16x⁻² − 8) dx = (3/2)x² − 16/x − 8x
- 2At x = 4: 24 − 4 − 32 = −12; at x = 1: 3/2 − 16 − 8 = −45/2
- 3Area under curve from 1 to 4 = −12 − (−45/2) = 21/2
- 4Area of trapezium under PQ = ½ × (11 + 5) × 3 = 24
- 5Area of R = 24 − 21/2 = 27/2
AnswerArea of R = 27/2 (13.5)
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