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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Area of a Region In Exercises 41 and 42, use integration to find the area of the triangular region having the given vertices.

( 0 , 0 ) , ( 4 , 0 ) , ( 4 , 4 )

To determine

To calculate: The area of the triangular region having the vertices (0,0), (4,0) and (4,4).

Explanation

Given Information:

The triangular region having the vertices (0,0), (4,0) and (4,4).

Formula used:

Area of a region bounded by two graphs is calculated using the following formula,

If f and g are continuous on [a,b] and g(x)f(x) for all x in [a,b], then the area of the region bounded by the graphs of f, g, x=a and x=b is given by

A=ab[f(x)g(x)]dx

The equation of a straight line passing through points (x1,y1) and (x2,y2) is,

yy1=(y2y1x2x1)(xx1)

Calculation:

Consider the triangular region having the vertices (0,0), (4,0) and (4,4). The triangle is shown as follows:

From the graph, area of triangle OAB is the required region. It is the area bounded by the functions of side OB and OA in the interval [0,4]

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