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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Evaluate the integral by interpreting it in terms of areas.

0 9 ( 1 3 x 2 ) d x

To determine

To evaluate:

The integral 0913x-2dx by interpreting it in terms of area.

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:

0913x-2dx

4) Calculation:

0913x-2dx can be interpreted as the area under the graph of

fx= 13x-2  between x= 0 and x=9

The graph of y=13x-2  is the line with the slope 13 as shown in the figure below,

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