Evaluate (int_{frac{1}{2}}^{1} frac{x^{3} – 4}{x^{3}} mathrm {d} x).
-
A.
-5.5 -
B.
-2.0 -
C.
2.0 -
D.
5.5
Correct Answer: Option A
Explanation
(int_{frac{1}{2}}^{1} frac{x^{3} – 4}{x^{3}} mathrm {d} x equiv int_{frac{1}{2}}^{1} 1 – frac{4}{x^{3}} mathrm {d} x).
= (int_{frac{1}{2}}^{1} 1 – 4x^{-3} mathrm {d} x).
= (left. x – frac{4x^{-2}}{-2}right |_{frac{1}{2}}^{1} = left. x + frac{2}{x^{2}}right |_{frac{1}{2}}^{1})
= ((1 + 2) – (frac{1}{2} + 8) = 3 – 8.5 = -5.5)