A particle moves along a number line with velocity at time t given by the formula $v(t) = t\text{ 1n}(t + 1)$.

1. Use a $5$-term midpoint Riemann sum to estimate the displacement of the particle over the interval from $t = 0$ to $t = 4$.

   Hint (a):

   General setup for a midpoint Riemann sum:

2. Estimate the same displacement using the Trapezoidal Rule with $5$ trapezoids.

   Hint (b):

   General setup for Trapezoidal sum on $[a, b]$: