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Chapter 14: Q. 5 (page 903)

In Problems 5 and 6, refer to the illustration. The interval [1,3]is partitioned into two sub intervals [1,2]and .[2,3]

Approximate the area A choosing u as the left endpoint of each sub interval.

Short Answer

Expert verified

The area of the given region by using the left end point of each sub interval is 3

Step by step solution

01

Step 1. Given

From the graph,

f(1)=1;f(2)=2f(3)=4

The interval [1,3]is partitioned into two sub intervals [1,2]and [2,3]

02

Step 2. Find the area by using partition formula

Area A = area of first rectangle + area of second rectangle

=f(u1)b-a2+f(u2)b-a2

03

Step 3. Substitute the values

Substitute the values and find the area,

A=f(1)3-12+f(2)3-12=1(1)+2(1)=3

The area of the region is 3

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