Integrate \((x - \frac{1}{x})^{2}\) with respect to x.
FURTHER MATHEMATICS
WAEC 2016
Integrate \((x - \frac{1}{x})^{2}\) with respect to x.
- A. \(\frac{1}{3}(x - \frac{1}{x})^{3} + c\)
- B. \(\frac{x^{3}}{3} - x\sqrt{\frac{1}{x^{3}}} + c\)
- C. \(\frac{x^{3}}{3} - 2x + \frac{1}{x^{3}} + c\)
- D. \(\frac{x^3}{3} - 2x - \frac{1}{x} + c\)
Correct Answer: D. \(\frac{x^3}{3} - 2x - \frac{1}{x} + c\)
Explanation
\((x - \frac{1}{x})^{2} = x^2 - 2 + \frac{1}{x^2}\)
\(\int (x^2 + \frac{1}{x^2} - 2) \mathrm {d} x\)
= \(\int (x^2 + x^{-2} - 2) \mathrm {d} x\)
= \(\frac{x^3}{3} - 2x - \frac{1}{x}\)
Post an Explanation Or Report an Error
If you see any wrong question or answer, please leave a comment below and we'll take a look. If you doubt why the selected answer is correct or need additional more details? Please drop a comment or Contact us directly. Your email address will not be published. Required fields are marked *