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# When a rubber-band is stretched by a distance $x$, it exerts a restoring force of magnitude $F=ax+bx^2$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber-band by $L$ is :

$\begin{array}{1 1}(A)\;\large\frac{aL^2}{2} +\frac{bL^3}{3} \\ (B)\;\large\frac{1}{2} \bigg(\frac{aL^2}{2} +\frac{bL^3}{3}\bigg) \\(C)\;aL^2+bL^3 \\(D)\;\frac{1}{2}(aL^2+bL^3) \end{array}$

The work done in stretching the unstretched rubber-band by $L$ is : $\large\frac{aL^2}{2} +\frac{bL^3}{3}$
Hence A is the correct answer.