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. units
• C. $4$ sq. units
• D. None of these

Answer 1

The correct option is A $\frac{17}{4}$ sq. units

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