Answer
Divergent
Work Step by Step
Let \[I=\int_{-\infty}^{\infty}(y^3-3y^2)dy\;\;\;\ldots (1)\]
\[I=\int_{-\infty}^{0}(y^3-3y^2)dy+\int_{0}^{\infty}(y^3-3y^2)dy\;\;\ldots (2)\]
Let \[I_1=\int_{-\infty}^{0}(y^3-3y^2)dy\;\;\;\ldots(3)\]
\[I_1=\lim_{t\rightarrow -\infty}\int_{t}^{0}(y^3-3y^2)dy\]
\[I_1=\lim_{t\rightarrow -\infty}\left[\frac{y^4}{4}-y^3\right]_{t}^{0}\]
\[I_1=\lim_{t\rightarrow -\infty}\left[0-\left(\frac{t^4}{4}-t^3\right)\right]\]
$\;\;\;\;\;\;\;\;\;$ Does not exist
Since limit on R.H.S. of (3) does not exist
$\Rightarrow$ $I_1$ is divergent
From (2)
Consequently $I$ is divergent.
