Q66 / 125 · BITSAT 2019 · Mathematics

Area bounded by two branches of the curve ${(y - x)}^{2} = x^{3}$ and $x = 1$ is

Solution

Given, curve is ${(y - x)}^{2} = x^{3}$

$\Rightarrow y - x = \pm x \sqrt{x}$

$\Rightarrow y = x \pm x \sqrt{x}$

$∴$ Area bounded $= |\int_{0}^{1} \{(x + x \sqrt{x}) - (x - x \sqrt{x})\} d x|$

$= |2 \int_{0}^{1} x^{3 / 2} d x| = \frac{4}{5} sq unit$

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