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JAMB 1999 · UME · Q34

Evaluate ∫−21(x−1)2 dx\displaystyle\int_{-2}^{1} (x - 1)^2\,dx.

Worked solution (try it first)
  1. (x−1)2(x - 1)^2 integrates to (x−1)33\frac{(x - 1)^3}{3}.
  2. At x=1x = 1 this is 0.
  3. At x=−2x = -2 it is (−3)33=−9\frac{(-3)^3}{3} = -9.
  4. Subtract: 0−(−9)=90 - (-9) = 9, option C.

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