Answer:
Option C
Explanation:
We know that change in potential energy ofa system corresponding to a conservative internal force as
$U_{f}-U_{i}=-W=-\int_{i}^{f} F.dr$
Given, $F= ax+bx^{2}$
We know that work done in stretching the rubber band by L is
|dW|= |F dx|
$|W|=\int_{0}^{L} (ax+bx^{2})dx$
= $\left[ \frac{ax^{2}}{2}\right]_0^L+\left[\frac{bx^{3}}{3}\right]_0^L$
= $\left[ \frac{aL^{2}}{2}-\frac{a\times (0)^{2}}{2}\right]$ + $\left[ \frac{bL^{3}}{3}-\frac{b\times (0)^{3}}{3}\right]$
$|W|=\frac{aL^{2}}{2}+\frac{bL^{3}}{3}$
