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...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 5.4, Problem 44E

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 43E

Chapter 5.4, Problem 45E

Chapter 5 Solutions

CALCULUS (CLOTH)

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

Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - 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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.