Explanation Given: f ( x ) = sin 3 x − x Formula used: A r e a = ∫ a b f ( x ) d x , [ a , b ] = F ( b ) − F ( a ) Calculation: The graph of the function is as shown in the following figure: It is evident from the graph that its value is positive at 0.5 and negative at 1. So, the positive root lies in the range[0.5,1]. Applying the bisection method, we get the positive root as x = 0.760 . ∫ 0 0.760 ( sin 3 x − x ) d x = [ − 1 3 cos 3 x − x 2 2 ] 0 0...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 5.4, Problem 46E

To determine

We need to plot the function $f (x) = \sin 3 x - x$ .

We need to find the positive root of $f$ upto three decimal places.

We need to use the above result to find the area under the graph of $f$ in the first quadrant.

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Chapter 5.4, Problem 45E

Chapter 5.4, Problem 47E

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Chapter 5 Solutions

Calculus - Standalone book

Ch. 5.1 - Prob. 1PQ Ch. 5.1 - Prob. 2PQ Ch. 5.1 - Prob. 3PQ Ch. 5.1 - Prob. 4PQ Ch. 5.1 - Prob. 5PQ Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E

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We need to plot the function f ( x ) = sin 3 x − x . We need to find the positive root of f upto three decimal places. We need to use the above result to find the area under the graph of f in the first quadrant.

Solution Summary: The author explains how to determine the positive root of the function f by plotting it in the first quadrant.

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We need to plot the function $f (x) = \sin 3 x - x$ .

We need to find the positive root of $f$ upto three decimal places.

We need to use the above result to find the area under the graph of $f$ in the first quadrant.

Want to see the full answer?

Chapter 5 Solutions

We need to plot the function f ( x ) = sin 3 x − x . We need to find the positive root of f upto three decimal places. We need to use the above result to find the area under the graph of f in the first quadrant.

Solution Summary: The author explains how to determine the positive root of the function f by plotting it in the first quadrant.

Concept explainers

Videos

We need to plot the function f(x)=sin3x−x. We need to find the positive root of fupto three decimal places. We need to use the above result to find the area under the graph of fin the first quadrant.

Want to see the full answer?

Chapter 5 Solutions

We need to plot the function $f (x) = \sin 3 x - x$ .

We need to find the positive root of $f$ upto three decimal places.

We need to use the above result to find the area under the graph of $f$ in the first quadrant.