WMA12/01 Jan 2020, Question 4: Definite Integrals and Areas
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 6 marks
The question, in short
Find the exact area of the region R bounded by the curve y = 2x² + 7, the y-axis and the line y = 17, for x ≥ 0.
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Solution · 6 marks
- 1Curve meets y = 17 when 2x² + 7 = 17, so x² = 5, x = √5
- 2∫ (2x² + 7) dx = (2/3)x³ + 7x
- 3Area under curve from 0 to √5 = (2/3)(5√5) + 7√5 = (31/3)√5
- 4Rectangle = 17 × √5 = 17√5
- 5Area of R = 17√5 − (31/3)√5 = (20/3)√5
AnswerArea of R = (20/3)√5
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