Question 39

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Jambmaths question: 

Integrate $\frac{{{x}^{2}}-\sqrt{x}}{x}$ with respect x

Option A: 

$\frac{2({{x}^{2}}-x)}{3x}+k$

Option B: 

$\frac{{{x}^{2}}-\sqrt{x}}{{{x}^{2}}}+k$

Option C: 

$\frac{{{x}^{2}}}{2}-2\sqrt{x}+k$

Option D: 

$\frac{{{x}^{2}}}{2}-\sqrt{x}+k$

Jamb Maths Solution: 

$\begin{align}  & \int{\frac{{{x}^{2}}-\sqrt{x}}{x}}dx=\int{\left( \frac{{{x}^{2}}}{x}-\frac{\sqrt{x}}{x} \right)dx} \\ & =\int{(x-{{x}^{-\tfrac{1}{2}}})dx} \\ & =\frac{{{x}^{2}}}{2}-2{{x}^{\tfrac{1}{2}}}+k \\ & =\frac{{{x}^{2}}}{2}-2\sqrt{x}+k \end{align}$

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