Solved: The Fresnel function is defined by the integral (a) Graph the function on the

Chapter 0, Problem 5

(choose chapter or problem)

The Fresnel function S is defined by the integral \(S(x)=\int_{0}^{x} \sin \left(\frac{\pi t^{2}}{2}\right) d t\) .

(a) Graph the function \(y=\sin \left(\frac{\pi x^{2}}{2}\right)\) on the interval [0,3].

(b) Use the graph in part (a) to sketch the graph of S on the interval [0,3].

(c) Locate all relative extrema of S on the interval (0,3).

(d) Locate all points of inflection of S on the interval (0,3).

Text Transcription:

S(x)=int_0^x sin(pi t^2/2) dt

y=sin(pi x^2/2)