In Problems 3 to 12, find the exponential Fourier transform of the given f ( x ) and write f ( x ) as a Fourier integral [that is, find g ( α ) in equation ( 12.2 ) and substitute your result into the first integral in equation ( 12.2 ) ] . f ( x ) = 1 , π / 2 < | x | < π 0 , otherwise
In Problems 3 to 12, find the exponential Fourier transform of the given f ( x ) and write f ( x ) as a Fourier integral [that is, find g ( α ) in equation ( 12.2 ) and substitute your result into the first integral in equation ( 12.2 ) ] . f ( x ) = 1 , π / 2 < | x | < π 0 , otherwise
In Problems 3 to 12, find the exponential Fourier transform of the given
f
(
x
)
and write
f
(
x
)
as a Fourier integral [that is, find
g
(
α
)
in equation
(
12.2
)
and substitute your result into the first integral in equation
(
12.2
)
]
.
Find the Fourier coefficients of the function
3
f(x) = sin(10x) cos(x).
QUESTION 4
Use the substitution u = (x – 1) to find
dr,
giving your answer in terms of x.
00
2. Use the definition of Fourier Transform, i.e. the equation f(t) =LF(@) elwt dw to
find the Fourier integral representation of the function defined by:
f(t) = }0
(1 - 1sis1
It| > 1
Fundamentals of Differential Equations and Boundary Value Problems
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