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

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

  • A.
    (-1frac{1}{2})
  • B.
    (-frac{15}{16})
  • C.
    (frac{15}{16})
  • D.
    (1frac{1}{2})
Correct Answer: Option D
Explanation

(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 = 1frac{1}{2})

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