Q. The area of the region bounded by the curve $y = x^3$, and the lines, $y = 8,$ and $x = 0,$ is
AIEEEAIEEE 2012Application of Integrals
Solution:
Required Area $\int\limits^{8}_{{y=0}}y^{1/3}dy$
$=\frac{y^{\frac{1}{3}+1}}{\frac{1}{3}+1}|^8_0$ $=\frac{3}{4}\left(y^{\frac{4}{3}}\right)|^8_0$
$=\frac{3}{4}\left[\left(8\right)^{\frac{4}{3}}-0\right]=\frac{3}{4}\left[2^{4}\right]$
$=\frac{3}{4}\times61=12$ sq. unit.
