Question

The area (in sq. units) enclosed by the figure described by the equation $x^4+1=2x^2+y^2$ is

• A. $\frac{8}{3}$
• B. $\frac{4}{3}$
• C. $\frac{7}{3}$
• D. $\frac{13}{3}$

Answer 1

The correct option is A $\frac{8}{3}$

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


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