# When a certain rubber band is stretched a distance of x, it exerts a restoring force of magnitude

1. F = ax + bx2
2. Where a and b are constants. The work done in stretching this rubber band from x = 0 to x = L is
1. aL2 + bLx3
2. aL + 2bL2
3. a + 2bL
4. bL
5. aL2/2 + bL3/3

The work done in stretching this rubber band from x = 0 to x = L is aL2/2 + bL3/3

### Helping Concept:

1. Work done is given by
2. $\dpi{80}&space;\fn_jvn&space;W&space;=&space;\int_{0}^{L}&space;F&space;dx$
3. $\dpi{80}&space;\fn_jvn&space;W&space;=&space;\int_{0}^{L}(ax&space;+&space;bx^{2})dx$
4. $\dpi{80}&space;\fn_jvn&space;W&space;=&space;\int_{O}^{L}(ax)dx&space;+&space;\int_{0}^{L}(bx^{2})dx$
5. $\dpi{80}&space;\fn_jvn&space;W&space;=&space;a\left&space;|&space;\frac{x^{2}}{2}&space;\right&space;|_{0}^{L}&space;+&space;b\left&space;|&space;\frac{x^{3}}{3}&space;\right&space;|_{0}^{L}$
6. Substituting upper and lower limits
7. $\dpi{80}&space;\fn_jvn&space;W&space;=&space;\frac{aL^{2}}{2}&space;+&space;\frac{bL^{3}}{3}$