Chapter 14.5, Problem 6AYU

To determine

To solve: The interval $\left[1,3\right]$ is partitioned into two subintervals $\left[1,2\right]$$\left[2,3\right]$.

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

Answer to Problem 6AYU

Solution:

The area $A$ is 6.

Explanation of Solution

Given:

The interval $\left[1,3\right]$ is partitioned into two subintervals $\left[1,2\right]$$\left[2,3\right]$.

Calculation:

Each of length 1, and choose $u$ as right end point.

The area $A$ is approximated as

$A=f\left(2\right)1+f\left(3\right)1$

$=2\left(1\right)+4\left(1\right)$

$=6$