Express the limit as a definite integral on the given interval.lim n→∞ ni = 1[2(xi*)3 − 8xi*]Δx,    [2, 4]

The given limit is the definition of a Riemann sum for a definite integral. The function to be integrated is f(x) = 2x^3 - 8x, and the interval of integration is [2, 4].

The Riemann sum is given by:

lim n→∞ Σ (from i=1 to n) f(xi*) Δx

where xi* is a sample point in the i-th subinterval, and Δx = (b - a)/n is the width of each subinterval in the partition of [a, b].

As n approaches infinity, the Riemann sum becomes the definite integral of f(x) from a to b. Therefore, the limit can be expressed as the definite integral:

∫ (from 2 to 4) (2x^3 - 8x) dx