   Chapter 4.2, Problem 39E

Chapter
Section
Textbook Problem

# Evaluate the integral by interpreting it in terms of areas. ∫ − 4 3 | 1 2 x | d x

To determine

To evaluate:

The integral -4312xdx by interpreting it in terms of areas.

Explanation

1) Concept:

A definite integral can be interpreted as a net area, that is, 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:

-4312xdx

4) Calculation:

The given integral -4312xdx can be interpreted as the area under the graph of

fx= 12x  between x= -4 and x=3

The graph of fx= 12x is shown below

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