Find the area of the shaded region bounded by $y = - 2, y = 1$ and $x = y^{3}$ .

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Solution

The required area is given by,
$A = \int_{- 2}^{1} x d y$
$= \int_{- 2}^{0} - y^{3} d y + \int_{0}^{1} y^{3} d y$
$= {[\frac{- y^{4}}{4}]}_{- 2}^{0} + {[\frac{y^{4}}{4}]}_{0}^{1}$
$= \frac{16}{4} + \frac{1}{4}$
$= \frac{17}{4}$

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Find the area of the shaded region bounded by y=−2,y=1 and x=y3.

The required area is given by, A=∫1−2xdy =∫0−2−y3dy+∫10y3dy =[−y44]0−2+[y44]10 =164+14 =174

Find the area of the shaded region bounded by $y = - 2, y = 1$ and $x = y^{3}$ .

The required area is given by,
$A = \int_{- 2}^{1} x d y$
$= \int_{- 2}^{0} - y^{3} d y + \int_{0}^{1} y^{3} d y$
$= {[\frac{- y^{4}}{4}]}_{- 2}^{0} + {[\frac{y^{4}}{4}]}_{0}^{1}$
$= \frac{16}{4} + \frac{1}{4}$
$= \frac{17}{4}$