JAMB 1994 · UME · Q42

Evaluate $\displaystyle\int_{-1}^{1} (2x + 1)^2\,dx$ .

Worked solution (try it first)

Expand the square: $(2x + 1)^2 = 4x^2 + 4x + 1$ .
Integrate: $\left[\frac43x^3 + 2x^2 + x\right]_{-1}^{1}$ .
At $x = 1$ this is $\frac43 + 3 = \frac{13}{3}$ .
At $x = -1$ it is $-\frac43 + 2 - 1 = -\frac13$ .
Subtract: $\frac{13}{3} - \left(-\frac13\right) = \frac{14}{3}$
$= 4\frac23$ , option D.