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 constant. The work done in stretching the unstretched rubber band by L is

Q: 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 constant. The work done in stretching the unstretched rubber band by L is

(a) $ aL^2 + bL^3 $

(b) $ \frac{1}{2} (aL^2 + bL^3 )$

(c) $ \frac{aL^2}{2} + \frac{bL^3}{3} $

(d) $ \frac{1}{2} (\frac{aL^2}{2} + \frac{bL^3}{3}) $

Ans: (c)