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CalculusCalculus (MindTap Course List)8th Edition

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Chapter 4.3, Problem 64E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
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Problem 17E
Problem 18E
Problem 19E
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Problem 21E
Problem 22E
Problem 23E
Problem 24E
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Problem 28E
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Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
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Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 78E
Problem 79E
Problem 80E
Problem 81E
Problem 82E
Problem 83E
Problem 84E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

The sine integral function

Si ( x ) = ∫ 0 x sin t t   d t

is important in electrical engineering. [The integrand f ( t ) = ( sin t ) / t is not defined when t = 0 , but we know that its limit is 1 when t → 0 . So we define f ( 0 ) = 1 and this makes f a continuous function everywhere.]

(a) Draw the graph of Si.

(b) At what values of x does this function have local maximum values?

(c) Find the coordinates of the first inflection point to the right of the origin.

(d) Does this function have horizontal asymptotes?

(e) Solve the following equation correct to one decimal place:

∫ 0 x sin t t  dt=1

To determine

(a)

To draw:

Graph of integral Si

Explanation

Concept:

Use Computer Algebra System to draw a graph

Calculation:

By using Mathematica,

Use below command:

si=Integrate[Sin[t]/t,{t,0,x}]

Output:

S

To determine

(b)

To find:

Values of x where the function has local maximum values

To determine

(c)

To find:

Co-ordinates of the first inflection point to the right of origin

To determine

(d)

To check:

Whether the given function has horizontal asymptotes

To determine

(e)

To solve:

The given equation by using the graph

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