Question

The area of the figure bounded by two branches of the curve (y – x)² = x³ and the straight line x = 1 is -

• A. 1/3 sq. units
• B. 4/5 sq. units
• C. 5/4 sq. units
• D. 3 sq. units

Answer 1

Answer: (B)

4/5 sq. units

Answer 2

Given curve is (y – x)² = x³

Ž y – x = ± x $\sqrt { \mathrm { x } }$ or y = x ± x

\ Required area = $\mid \int _ { 0 } ^ { 1 } [ ( x + x \sqrt { x } - ( x - x \sqrt { x } ) ] d x \mid$ =

= sq. units.