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## Homework Statement

Use the mean value theorem to show that [itex] \frac{b^3-a^3}{b-a} = \sum_{j=1}^{n}d_j^2 (x_j - x_{j-1}) \text{where} x_{j-1} < d_j < x_j .[/itex]

## Homework Equations

The mean value theorem states that if f is continuous on [a,b] and differentiable on (a,b) then there exists a c in (a,b) such that [itex]f(c) = \frac{f(b)-f(a)}{b-a} [/itex].