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WAEC Further Mathematics 2008 Question 20

Question 20

Integration

Given that f′(x) = 3x2 − 6x + 1 and f(3) = 5, find f(x).

  1. A.f(x) = x3 − 3x + x + 20
  2. B.f(x) = x3 − 3x2 + x + 31
  3. C.f(x) = x3 − 3x2 + x + 2
  4. D.f(x) = x3 − 3x2 + x − 13
Show the answer and explanation

Answer: C (f(x) = x3 − 3x2 + x + 2)

Explanation

Integrate: f(x) = x3 − 3x2 + x + c. f(3) = 27 − 27 + 3 + c = 5, so c = 2.