### Home > CALC > Chapter 5 > Lesson 5.5.2 > Problem5-172

5-172.

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 $t = 4$.

General setup for a midpoint Riemann sum:

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

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