Question 39

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Jambmaths question: 

Evaluate $\int_{1}^{2}{({{x}^{2}}-4x)dx}$

Option A: 

$\tfrac{11}{3}$

Option B: 

$\tfrac{3}{11}$

Option C: 

$-\tfrac{3}{11}$

Option D: 

$-\tfrac{11}{3}$

Jamb Maths Solution: 

$\begin{align}  & \int_{1}^{2}{({{x}^{2}}-4x)dx}=\left[ \frac{{{x}^{3}}}{3}-\frac{4{{x}^{2}}}{2} \right]_{1}^{2}=\left[ \frac{{{x}^{3}}}{3}-2{{x}^{2}} \right]_{1}^{2} \\ & \int_{1}^{2}{({{x}^{2}}-4x)dx}=\left( \frac{{{2}^{3}}}{3}-2{{(2)}^{2}} \right)-\left( \frac{1}{3}-2(1) \right) \\ & \int_{1}^{2}{({{x}^{2}}-4x)dx}=\left( \frac{8}{3}-8 \right)-\left( \frac{1}{3}-2 \right)=\left( \frac{8-24}{3} \right)-\left( \frac{1-6}{3} \right) \\ & \int_{1}^{2}{({{x}^{2}}-4x)dx}=\frac{-16}{3}+\frac{5}{3}=-\frac{11}{3} \\\end{align}$

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