When a Rubber Band is stretched by a distance x, it exerts a restoring fore of magnitude  F  =    ax+bx2   where a and b are constants.   The work done in stretching the unstretched rubber band by L−  is

Given restoring Force  of Rubber Band is F   =   ax  +bx2---(1) work done in stretching the Rubber Band is dw=F.dx length extended from 0 to L ∴ work done =W=∫0Ldw W=∫0LF.dx substitute eqn(1) W=∫0L  (ax  +bx2).dx  W=    a (x22)0L+b(x33)0L ∴    W   =   aL22+bL33=work done in stretching Rubber Band from 0 to L