   Chapter 4.2, Problem 40E

Chapter
Section
Textbook Problem

# Evaluate the integral by interpreting it in terms of areas. ∫ 0 1 | 2 x − 1 |   d x

To determine

To evaluate:

The integral 012x-1dx by interpreting it in terms of areas.

Explanation

1) Concept:

A definite integral can be interpreted as a net area, that is, as a difference of areas;

abf(x)dx=A1-A2

where A1 is the region above x- axis and below the graph of f, and A2 is the region below x- axis and above the graph of f.

2) Formula:

Area of a triangle : A=12bh

where b is the base and  h   is the height.

3) Given:

012x-1dx

4) Calculation:

The given integral 012x-1dx can be interpreted as the area under the graph of

fx= | 2x-1|  between x= 0 and x=1 that means sum of the areas of the two shaded triangles

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