§4.2 Riemann sums

Introduction

Sigma Notation

Riemann Sums

When the function is sometimes negative

$\displaystyle \sum_{k=1}^{5} (k^2 + 2)$

$\displaystyle \sum_{i=3}^{6} (2i-1)$

Building on your work in (a), estimate the total change in position of the object on the interval $[1,5]$.

Expand and evaluate the sigma sum $\sum_{k=1}^{5}(k^2 + 2)$ term by term.

Expand and evaluate the sigma sum $\sum_{i=3}^{6}(2i - 1)$ term by term.

For a positive increasing function on $[a, b]$, the left sum $L_n$ and right sum $R_n$ satisfy

For the walker's velocity table, the right endpoint sum with four rectangles of width $0.5$ is $R_4 = \frac{335}{48}$. Compute its decimal value, rounded to three decimals.

A velocity function sampled at midpoints on $[1,5]$ with five rectangles gives $M_5 = -\frac{36}{25}$. Report this estimate of the total change in position, rounded to two decimals.

The sum $\sum_{i=1}^{6}\frac{1}{2^i}$ equals $\frac{63}{64}$, which is strictly less than $1$.