The area (in sq. units) of the region bounded by the curve $y = 2x^3$, x-axis and ordinates $x = -1$ and $x = 1$ is.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1
Given curve $y=2x^3$.
Required area between $x=-1$ and $x=1$ with x-axis.
Since the curve is odd, area is symmetric about origin.
Area $=2\int_{0}^{1}2x^3dx$
$=4\int_{0}^{1}x^3dx$
$=4\left[\frac{x^4}{4}\right]_0^1$
$=4\left(\frac{1}{4}-0\right)$
$=1$
$1$ square unit