Chapter 14.5, Problem 7AYU

To determine

To solve: The interval $\left[0,8\right]$ is partitioned into four subintervals $\left[0,2\right]$, $\left[2,4\right]$, $\left[4,6\right]$ and $\left[6,8\right]$.

Approximate the area $A$ choosing $u$ as the left endpoint of each subinterval.

Answer to Problem 7AYU

Solution:

The area $A$ is 56.

Explanation of Solution

Given:

The interval $\left[0,8\right]$ is partitioned into four subintervals $\left[0,2\right]$, $\left[2,4\right]$, $\left[4,6\right]$ and $\left[6,8\right]$.

Calculation:

Each of length 2, and choose $u$ as left end point.

The area $A$ is approximated as

$A=f\left(0\right)2+f\left(2\right)2+f\left(4\right)2+f\left(6\right)2$

$=10\left(2\right)+6\left(2\right)+7\left(2\right)+5\left(2\right)$

$=20+12+14+10$

$=56$