JAMB - Mathematics (2007 - No. 10)
Integrate \(\frac{x^2 -\sqrt{x}}{x}\) with respect to x
\(\frac{x^2}{2}-2\sqrt{x}+K\)
\(\frac{2(x^2 - x)}{3x}+K\)
\(\frac{x^2}{2}-\sqrt{x}+K\)
\(\frac{(x^2 - x)}{3x}+K\)
توضیح
\(\int \frac{x^2 -\sqrt{x}}{x} = \int \frac{x^2}{x} - \frac{x^{\frac{1}{2}}}{x}\\
\int x - x^{\frac{-1}{2}}\\
=\left(\frac{1}{2}\right)x^2 - \frac{x^{\frac{1}{2}}}{\frac{1}{2}}+K\\
=\frac{x^2}{2}-2x^{\frac{1}{2}}+K\\
=\frac{x^2}{2}-2\sqrt{x}+K\)
\int x - x^{\frac{-1}{2}}\\
=\left(\frac{1}{2}\right)x^2 - \frac{x^{\frac{1}{2}}}{\frac{1}{2}}+K\\
=\frac{x^2}{2}-2x^{\frac{1}{2}}+K\\
=\frac{x^2}{2}-2\sqrt{x}+K\)