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

5-172.

A particle moves along a number line with velocity at time

*t*given by the formula*v*(*t*) =*t*ln(*t*+ 1). Homework Help ✎Use a 5-term midpoint Riemann sum to estimate the displacement of the particle over the interval from

*t*= 0 to*t*= 4.Estimate the same displacement using the Trapezoidal Rule with 5 trapezoids.

General setup for a midpoint Riemann sum:

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