Question

What is the area bounded by the curves $|y|=1-x^2$?

• A. 4/3 square units
• B. 8/3 square units
• C. 4 square units
• D. 16/3 square units

Answer 1

The correct option is B 8/3 square units

$|y|=1-x^2$

$|y|\ge 0$

$\therefore 1-x^2\ge 0$

$\therefore x=[-1,1]$

$|y|=1-x^2$

Above equation represents 2 curves are $y=1-x^2$ and $y=x^2-1$

Area $={\int }_{-1}^1\left(\right(1-x^2)-(x^2-1\left)\right)dx$

$=2{\int }_{-1}^1(1-x^2)dx$

$=4{\int }_0^1(1-x^2)dx$

$=4{[x-\frac{x^3}{3}]}_0^1$

$=4(1-\frac{1}{3})$

$=\frac{8}{3}sq.units$