Question

The area of the region bounded by the curve y = 2x – x² and x – axis is

A)$\frac{2}{3}sq.units$  

B) $\frac{4}{3}sq.units$ 

C) $\frac{5}{3}sq.units$ 

D)$\frac{8}{3}sq.units$

Answer 1

Correct answer is $\frac{4}{3}sq.units$ 

Explaination::

Given curve is $y=2x-x^2$  or $(x-1{)}^2=-(y-1)$ 

The curve cut the x -axis at (0,0) and (2,0) .

$\therefore Requiredarea={\int }_0^{2}ydx$

$={\int }_0^2(2x-x^2)dx={[x^2-\frac{x^3}{3}]}_0^2$

$=4-\frac{8}{3}=\frac{4}{3}squnit$