Explanation 1) Concept: A definite integral can be interpreted as a net area, that is, as a difference of areas; ∫ a b f ( x ) d x = A 1 - A 2 where A 1 is the region above x - a x i s and below the graph of f , and A 2 is the region below x - a x i s and above the graph of f . 2) Formula: Area of a triangle : A = 1 2 b h where b is the base and h is the height. 3) Given: ∫ 0 1 2 x - 1 d x 4) Calculation: The given integral ∫ 0 1 2 x - 1 d x can be interpreted as the area under the graph of f x = | 2 x - 1 | between x = 0 a n d x = 1 that means sum of the areas of the two shaded triangles

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Author: James Stewart

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Chapter 4.2, Problem 40E

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To evaluate:

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

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Chapter 4.2, Problem 39E

Chapter 4.2, Problem 41E

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The integral ∫ 0 1 2 x - 1 d x by interpreting it in terms of areas.

Solution Summary: The author explains that a definite integral can be interpreted as the area under the graph of f(x)=|2x-1|.

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To evaluate:

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

Want to see the full answer?

Chapter 4 Solutions

The integral ∫ 0 1 2 x - 1 d x by interpreting it in terms of areas.

Solution Summary: The author explains that a definite integral can be interpreted as the area under the graph of f(x)=|2x-1|.

Concept explainers

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To evaluate: The integral ∫012x-1dx by interpreting it in terms of areas.

Want to see the full answer?

Chapter 4 Solutions

To evaluate:

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