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
Answer & explanation
Correct answer: option 2
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.