Question Bank - Mathematics

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The anti-derivative of \(\sqrt x - \frac {1}{\sqrt x}\) is equal to

A.
\(\rm \frac{2}{3}x^{\frac{3}{2}}+2x^\frac{1}{2} + C\)
B.
\(\rm \frac{2}{3}x^{\frac{3}{2}}-2x^\frac{1}{2} + C\)
C.
\(\rm \frac{2}{3}x^{\frac{3}{2}}-x^\frac{1}{2} + C\)
D.
None of the above

Solution:

Concept:Some useful formulas are:\(\rm ? x^n dx = \frac {(x^{n+1})} {(n+1)} +C; \ n?1\)Calculation:\(\rm \int(\sqrt x - \frac {1}{\sqrt x})\ dx\)= \(\rm \int\sqrt x \ dx - \int\frac {1}{\sqrt x}\ dx\)= \(\rm \frac{x^{(\frac{1}{2}+1)}}{\frac{1}{2}+1} - \frac{x^{(\frac{-1}{2}+1)}}{\frac{-1}{2}+1} + C\) , where C is the constant of integration= \(\rm \frac{2}{3}x^{\frac{3}{2}}-2x^\frac{1}{2} + C\)

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