In Problems 13 to 16, find the Fourier cosine transform of the function in the indicated problem, and write f ( x ) as a Fourier integral [use equation (12.15)]. Verify that the cosine integral for f ( x ) is the same as the exponential integral found previously. Problem 9. 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)]. 9.
In Problems 13 to 16, find the Fourier cosine transform of the function in the indicated problem, and write f ( x ) as a Fourier integral [use equation (12.15)]. Verify that the cosine integral for f ( x ) is the same as the exponential integral found previously. Problem 9. 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)]. 9.
In Problems 13 to 16, find the Fourier cosine transform of the function in the indicated problem, and write
f
(
x
)
as a Fourier integral [use equation (12.15)]. Verify that the cosine integral for
f
(
x
)
is the same as the exponential integral found previously.
Problem 9.
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)].
9.
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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