   Chapter 4.3, Problem 64E

Chapter
Section
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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