Question

The area of the region bounded by the curve $y=x^3$, and the lines, $y=8,$ and $x=0,$ is

• A. $8$
• B. $12$
• C. $10$
• D. $16$

Answer 1

Answer: (B)

Required Area $\underset{y=0}{\overset{8}{\int }}{y}^{1/3}dy$
$=\frac{y^{\frac{1}{3}+1}}{\frac{1}{3}+1}{|}_0^8$ $=\frac{3}{4}\left(y^{\frac{4}{3}}\right){|}_0^8$
$=\frac{3}{4}\left[{\left(8\right)}^{\frac{4}{3}}-0\right]=\frac{3}{4}\left[2^4\right]$
$=\frac{3}{4}\times 61=12$ sq. unit.