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 ) = { sin x , | x | < π / 2 0 , | x | > π / 2 Hint: In Problems 11 and 12, use complex exponentials.
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 ) = { sin x , | x | < π / 2 0 , | x | > π / 2 Hint: In Problems 11 and 12, use complex exponentials.
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
)
=
{
sin
x
,
|
x
|
<
π
/
2
0
,
|
x
|
>
π
/
2
Hint: In Problems 11 and 12, use complex exponentials.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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