The Fresnel function S ( x ) = ∫ 0 x sin ( 1 2 π t 2 ) d t was discussed in Example 4.3.3 and is used extensively in the theory of optics. Find ∫ S ( x ) d x . [Your answer will involve S ( x ) . ]
Solution Summary: The author explains the technique of integration by parts, which can be thought of as a rule corresponding to the product rule in differentiation.
The Fresnel function
S
(
x
)
=
∫
0
x
sin
(
1
2
π
t
2
)
d
t
was discussed in Example 4.3.3 and is used extensively in the theory of optics. Find
∫
S
(
x
)
d
x
.
[Your answer will involve
S
(
x
)
.
]
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY