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JEE Previous Year Question

$\int_{1}^{2} \frac{x ^{3} - 1}{x ^{2}} dx is equal to$

Topic: JEE PYQ

Answer: C. Full step-by-step solution below.

A $\frac{5}{3}$
B $\frac{3}{5}$
C $1$
D $-1$

Correct answer: C

Solution

(c) Let I = \int_{1}^{2} \frac{x ^{3} - 1}{x ^{2}} dx = \int_{1}^{2} (x - \frac{1}{x ^{2}}) dx = (\frac{x ^{2}}{2} + \frac{1}{x}) = ((\frac{4}{2} + \frac{1}{2}) - (\frac{1}{2} + 1)) = \frac{5}{2} - \frac{3}{2} = 1.

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