WMA11/01 Oct 2020, Question 9: Integration: Undoing Differentiation
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks
The question, in short
A curve y = f(x) passes through (9, 10) and has derivative 27x² − (21x³ − 5x)/(2√x) for x > 0; find f(x), simplifying each term.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 6 marks
- 1(21x³ − 5x)/(2√x) = (21/2)x^(5/2) − (5/2)x^(1/2)
- 2f′(x) = 27x² − (21/2)x^(5/2) + (5/2)x^(1/2)
- 3f(x) = 9x³ − (21/2)(2/7)x^(7/2) + (5/2)(2/3)x^(3/2) + c = 9x³ − 3x^(7/2) + (5/3)x^(3/2) + c
- 4f(9) = 10: 6561 − 3(2187) + (5/3)(27) + c = 10
- 545 + c = 10, so c = −35
- 6f(x) = 9x³ − 3x^(7/2) + (5/3)x^(3/2) − 35
Answerf(x) = 9x³ − 3x^(7/2) + (5/3)x^(3/2) − 35
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