Question

The area enclosed by the curves described by the equation $x^4+1=2x^2+y^2$, is

• A. $3\text{sq. unit}$
• B. $\frac{8}{3}\text{sq. unit}$
• C. $\frac{7}{3}\text{sq. unit}$
• D. $\frac{10}{3}\text{sq. unit}$

Answer 1

The correct option is B $\frac{8}{3}\text{sq. unit}$

$x^4+1=2x^2+y^2$
$\Rightarrow y^2=(x^2-1{)}^2$
$\Rightarrow y=x^2-1$ or $y=1-x^2$


Required area $=4\underset{0}{\overset{1}{\int }}(1-x^2)dx$
$=4{[x-\frac{x^3}{3}]}_0^1=\frac{8}{3}\text{sq. unit}$