Question

The area of the region bounded by $y=-1,y=2,x=y^3$ and $x=0$ is

• A. $\frac{17}{4}$ sq units
• B. $\frac{1}{4}$ sq unit
• C. $4$ sq units
• D. None of these

Answer 1

Answer: (A)

Required area $=\underset{-1}{\overset{2}{\int }}\left|x_1\right|dy$

$=\underset{-1}{\overset{0}{\int }}\left(-x_1\right)dy+\underset{0}{\overset{2}{\int }}{x}_{1}dy$
$=-\underset{-1}{\overset{0}{\int }}{y}^{3}dy+\underset{0}{\overset{2}{\int }}{y}^{3}dy$
$=-{\left[\frac{y^4}{4}\right]}_{-1}^0+{\left[\frac{y^4}{4}\right]}_0^2$
$=\frac{1}{4}+4$
$=\frac{17}{4}$ sq units.