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JAMB 2012 · UTME · Q39

Evaluate ∫12(x2−4x) dx\displaystyle\int_1^2 (x^2 - 4x)\,dx.

Worked solution (try it first)
  1. Integrate: [x33−2x2]12\left[\frac{x^3}{3} - 2x^2\right]_1^2.
  2. At x=2x = 2: 83−8=−163\frac83 - 8 = -\frac{16}{3}.
  3. At x=1x = 1: 13−2=−53\frac13 - 2 = -\frac53.
  4. Subtract: −163+53=−113-\frac{16}{3} + \frac53 = -\frac{11}{3}, option D.

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