Jambmaths question:
Evaluate $\int_{2}^{3}{({{x}^{2}}-2x)dx}$
Option A:
4
Option B:
2
Option C:
$\frac{4}{3}$
Option D:
$\frac{1}{3}$
Jamb Maths Solution:
$\begin{align} & \int_{2}^{3}{({{x}^{2}}-2x)dx}=\left[ \frac{{{x}^{3}}}{3}-\frac{2{{x}^{2}}}{2} \right]_{2}^{3}=\left[ \frac{{{x}^{3}}}{3}-{{x}^{2}} \right]_{2}^{3} \\ & =\left[ \frac{{{3}^{3}}}{3}-{{3}^{2}} \right]-\left[ \frac{{{2}^{3}}}{3}-{{2}^{2}} \right]=\left[ 9-9 \right]-\left[ \frac{8}{3}-4 \right] \\ & =-\left[ \frac{8}{3}-4 \right]=4-\frac{8}{3}=\frac{12-8}{3}=\frac{4}{3} \end{align}$
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