4PM1/02 Nov 2021, Question 2: Volumes of Revolution
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 6 marks
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The question, in short
Find the exact volume of the solid made by rotating 360° about the x-axis the region between y = 4 − x² and y = x + 2, using algebraic integration.
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Solution · 6 marks
- 14 − x² = x + 2 gives x² + x − 2 = 0, (x − 1)(x + 2) = 0, x = 1, −2
- 2V = π∫ from −2 to 1 of (4 − x²)² dx − π∫ from −2 to 1 of (x + 2)² dx
- 3= π∫ from −2 to 1 of (x⁴ − 9x² − 4x + 12) dx
- 4= π[x⁵/5 − 3x³ − 2x² + 12x] from −2 to 1
- 5= 153π/5 − 9π = 108π/5
Answer108π/5
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