The area (in sq. units) of the region bounded by the curve $y=x^5$, the x-axis and the ordinates $x = -1$ and $x = 1$ is equal to

$\frac{1}{3}$

The correct answer is Option (2) → $\frac{1}{3}$

$y=x^5$ is an odd function

The region from $x=-1$ to $x=1$ is symmetric about the origin

Area bounded by the curve and the $x$-axis

$=2\int_{0}^{1} x^5\,dx$

$=2\left[\frac{x^6}{6}\right]_{0}^{1}$

$=2\cdot\frac{1}{6}$

$=\frac{1}{3}$

The required area is $\frac{1}{3}$ square units.