Q116 / 160 · TS EAMCET 2019 (03 May Shift 2) · Mathematics

The area of the region (in square units) bounded by the curves $y = x^{3}, y = x$ and $- 1 \leq x \leq 1$ , is

Solution

We have, $y = x^{3} & y = x$

The area bounded by the curves, $A = 2 \int_{0}^{1} (x - x^{3}) d x$

$= 2 {(\frac{x^{2}}{2} - \frac{x^{4}}{4})}_{0}^{1}$

$= 2 (\frac{1}{2} - \frac{1}{4}) = \frac{1}{2}$

Hence, the correct answer is option: 'B'.