Evaluate (int_{1}^{2} [frac{x^{3} – 1}{x^{2}}] mathrm {d} x).
-
A.
0.5 -
B.
1.0 -
C.
1.5 -
D.
2.0
Correct Answer: Option B
Explanation
(frac{x^{3} – 1}{x^{2}} equiv x – frac{1}{x^{2}} = x – x^{-2})
(int_{1}^{2} (x – x^{-2}) mathrm {d} x = (frac{x^{2}}{2} + frac{1}{x})|_{1}^{2})
= ((frac{2^{2}}{2} + frac{1}{2}) – (frac{1^{2}}{2} + frac{1}{1}))
= ((2 + frac{1}{2}) – (frac{1}{2} + 1))
= (2frac{1}{2} – 1frac{1}{2})
= (1.0)