Question 37

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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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