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JAMB Mathematics 2000 Question 39

Question 39

Integration

A function f(x) passes through the origin and its first derivative is 3x + 2. What is f(x)?

  1. A.y = (3/2)x2 + 2x
  2. B.y = (3/2)x2 + x
  3. C.y = 3x2 + x/2
  4. D.y = 3x2 + 2x
Show the answer and explanation

Answer: A (y = (3/2)x2 + 2x)

Explanation

Integrating 3x + 2 gives (3/2)x2 + 2x + c. Passing through the origin makes c = 0.