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When a rubber bandis streched by a dista...

When a rubber bandis streched by a distance `x` , if exerts resuring foprce of magnitube `F = ax + bx^(2)` where`a` and `b` are constant . The work in streached the unstreched rubber - band by `L` is

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The restoring force exerted by the rubber band when it is stretched by a distance 'x' is `F = ax + bx^(2)`.
The small amount of work done on the rubber band stretching through as small distance 'dx' is
`dW = Fdx (ax + bx^(2)) dx`
The total work done in stretching the unstretched rubber band by 'L' is.
`W = underset(0) overset(L) (int) Fdx = underset(0) overset(L) (int) (ax + bx^(2)) dx = underset(0) overset(L) (int) axdx + underset(0) overset(L) (int) bx^(2) dx`
`W = a[(x^(2))/(2)]_(0) ^(L) + b[(x^(3))/(3)]_(0)^(L) = (aL^(2))/(2) + (bL^(3))/(3)`.
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