Question on: JAMB Mathematics - 2007
Integrate (\frac{x^2 - \sqrt{x}}{x}) with respect to x
A
\(\frac{x^2 - \sqrt{x}}{x^2}\) + k
B
\(\frac{x^2 }{2}\) - \(\sqrt{x}\) + k
C
\(\frac{2(x^2 - x)}{3x}\) + k
D
\(\frac{x^2}{2}\) - 2\(\sqrt{x}\) + k
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Correct Option: D
Integrate (\frac{x^2 - \sqrt{x}}{x}) with respect to x
∫(\frac{x^2 - \sqrt{x}}{x})dx = ∫((\frac{x^2}{x} - \frac {\sqrt{x}}{x}))dx
= ∫(x - x(\frac{1}{2}))dx
= (\frac{x^2}{2}) - (\frac{x^{\frac{1}{2}}}{\frac{1}{2}}) + k
= (\frac{x^2}{2}) - 2(\sqrt{x}) + k
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