JAMB Mathematics 2019 Paper

Concept:Definite integration is evaluated by finding the antiderivative and applying the limits of integration.Explanation:Find the antiderivative of $2x^2 + x$. Increase each power by 1 and divide by the new power.$\int (2x^2 + x)\,dx = \frac{2x^3}{3} + \frac{x^2}{2} + C$Now evaluate from $x = -1$ to $x = 2$:$\left[\frac{2x^3}{3} + \frac{x^2}{2}\right]_{-1}^{2}$Substitute the upper limit $x=2$:$\frac{2(2)^3}{3} + \frac{(2)^2}{2} = \frac{16}{3} + 2 = \frac{22}{3}$Substitute the lower limit $x=-1$:$\frac{2(-1)^3}{3} + \frac{(-1)^2}{2} = -\frac{2}{3} + \frac{1}{2} = -\frac{1}{6}$Subtract the lower value from the upper value:$\frac{22}{3} - \left(-\frac{1}{6}\right) = \frac{22}{3} + \frac{1}{6} = \frac{44}{6} + \frac{1}{6} = \frac{45}{6} = \frac{15}{2} = 7\frac{1}{2}$Answer:The value of the integral is $7\frac{1}{2}$, which is option C.