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WAEC 2023 · Paper 1 · Q5

Evaluate: ∫01x(x2−2)2 dx\displaystyle\int_0^1 x(x^2 - 2)^2\,dx.

Worked solution (try it first)
  1. Expand the bracket: x(x4−4x2+4)=x5−4x3+4xx(x^4 - 4x^2 + 4) = x^5 - 4x^3 + 4x.
  2. Integrate each term: [x66−x4+2x2]01\left[\frac{x^6}{6} - x^4 + 2x^2\right]_0^1.
  3. Put in the limits: 16−1+2−0=76\frac{1}{6} - 1 + 2 - 0 = \frac{7}{6}.
  4. So the integral is 1161\frac{1}{6}, option C.

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