Evaluate \(\int_{1}^{2} \frac{4}{x^{3}} \mathrm {d} x\)

  • A \(-1\frac{1}{2}\)
  • B \(-\frac{15}{16}\)
  • C \(\frac{15}{16}\)
  • D \(1\frac{1}{2}\)
waec 2010furthermathematics

The correct answer is D. \(1\frac{1}{2}\)

\(\int \frac{4}{x^{3}} \mathrm {d} x = \int 4x^{-3} \mathrm {d} x\)

\(\frac{4x^{-3 + 1}}{-2} = -2x^{-2}|_{1}^{2} = \frac{-2}{x^{2}}|_{1}^{2}\)

= \(\frac{-2}{2^{2}}  - \frac{-2}{1^{2}} = -\frac{1}{2}  + 2 = 1\frac{1}{2}\)

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