4PM1/02 Jun 2020, Question 2: Volumes of Revolution
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 4 marks
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The question, in short
Find, using algebraic integration, the volume in terms of π and e of the solid formed when the region under y = e^(3x) from x = 0 to x = 3 is rotated 360° about the x-axis.
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Solution · 4 marks
- 1V = π ∫ from 0 to 3 of (e^(3x))² dx = π ∫ from 0 to 3 of e^(6x) dx
- 2= π[(1/6)e^(6x)] from 0 to 3
- 3= π((1/6)e¹⁸ − 1/6)
- 4= (π/6)(e¹⁸ − 1)
Answer(π/6)(e¹⁸ − 1)
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