Find the area of the region bounded by `y=-1,y=2, x=y^3 and x=0.`

Explanation

Required area `=int_{-1}^{2}|x_{1}| d y`


`=int_{-1}^{0}(-x_{1}) d y+int_{0}^{2} x_{1} d y`


`=-int_{-1}^{0} y^{3} d y+int_{0}^{2} y^{3} d y`


`=-[frac{y^{4}}{4}]_{-1}^{0}+[frac{y^{4}}{4}]_{0}^{2}=frac{1}{4}+4`


`=frac{17}{4}` sq. units