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Q.
The area of the region bounded by $y=-1,\, y=2,\, x=y^{3}$ and $x=0$ is
ManipalManipal 2012
Solution:
Required area $=\int\limits_{-1}^{2}\left| x_{1}\right| d y$
$=\int\limits_{-1}^{0}\left(-x_{1}\right) d y+\int\limits_{0}^{2} x_{1} d y$
$=-\int\limits_{-1}^{0} y^{3} d y+\int\limits_{0}^{2} y^{3} d y$
$=-\left[\frac{y^{4}}{4}\right]_{-1}^{0}+\left[\frac{y^{4}}{4}\right]_{0}^{2}$
$=\frac{1}{4}+4$
$=\frac{17}{4}$ sq units.
