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})