Question

The area (in sq. units) bounded by the curves $y=\sqrt{1-x^2}$ and $y=x^3-x$ is

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{4}$
• D. $\frac{3\pi }{2}$

Answer 1

The correct option is A $\frac{\pi }{2}$


$y=x^3-x$ is is an odd function which is symmetric about origin.
So, area bounded by this curve and $x-$ axis in second and fourth quadrant are equal and equal to $A_1$ (say)

Now, according to figure,
Required area $=$ Area of semi-circle above $x-$axis $+A_1-A_1$
$=\frac{1}{2}\times \pi (1{)}^2=\frac{\pi }{2}$