Integrate frac x 2 - sqrt x x with respect to x - JAMB Mathematics 2007 Question
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
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
∫\(\frac{x^2 - \sqrt{x}}{x}\)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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