Math 126 Section 5.4

The Fresnel Function is defined by the integral

f(x) =

We would like to see if Maple already knows about this function. We use the
help system by clicking on help and full text search. We type in Fresnel and find

the entry -

Function: FresnelS - The Fresnel Sine Integral

The Fresnel sine integral is defined as follows:
FresnelS(x) = int(sin(Pi/2*t^2), t=0..x)

We graph this function between -5 and 5 to get some idea
what it looks like.

> plot(FresnelS(x), x = -5 .. 5);

Problem 25
c) Use a graph to solve the following equation correct to one decimal place:

We want to find the x value where the Fresnel function has the value . 2
Looking at the graph above, it appears to be between 0 and 1 so we adjust the

range of our plot until we get close to the value we want. Using .6 to .8 for the
x range, it appears that the value .2 is reached when x = .74

> plot(FresnelS(x), x = .6 .. .8);

The Sine Integral Function

We would like to to use the sine integral function which is defined by the integral of



We use the Help system, full text search and type in sine integral function.

We find the entry

Function: Si - The Sine Integral etc.

Si(x) = int(sin(t)/t, t=0..x)

Here is a graph of this function when x runs from -30 to 30.

> plot(Si(x), x= -30 .. 30);