Explanation Given information: Calculation: First, let’s divide he interval [ 0 , 9 ] into three parts: I 1 = [ 0 , 3 ] I 2 = [ 3 , 5 ] I 3 = [ 5 , 9 ] Now we can see that we can calculate the given integral as a sum of the following integrals: ∫ ( f ( x ) − g ( x ) ) d x over interval I 1 That is ∫ 0 3 ( f ( x ) − g ( x ) ) d x (because the top part is f ( x ) and the bottom part is g ( x ) ) ∫ f

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

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Question

Chapter 6.1, Problem 52E

To determine

To express:

The area of the shaded region in Figure X as a sum of three integrals involving f(x) and g(x).

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Chapter 6.1, Problem 51E

Chapter 6.1, Problem 53E

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Chapter 6 Solutions

Calculus - Standalone book

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - 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To express: The area of the shaded region in Figure X as a sum of three integrals involving f ( x ) and g ( x ) .

Solution Summary: The author explains how to express the area of the shaded region in Figure X as a sum of three integrals.

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To express:

The area of the shaded region in Figure X as a sum of three integrals involving f(x) and g(x).

Want to see the full answer?

Chapter 6 Solutions

To express: The area of the shaded region in Figure X as a sum of three integrals involving f ( x ) and g ( x ) .

Solution Summary: The author explains how to express the area of the shaded region in Figure X as a sum of three integrals.

Concept explainers

Videos

To express: The area of the shaded region in Figure X as a sum of three integrals involving f(x) and g(x).

Want to see the full answer?

Chapter 6 Solutions

To express:

The area of the shaded region in Figure X as a sum of three integrals involving f(x) and g(x).