The Fourier integrals of two continuous functions f (x) and g(x) defined on R are given by 00 f(x) = / cos(wx) + 2л sin(wx) dw IT w3 and 00 / cos(w6x) w17 2л sin(wl6x)| dw. g(x) = W33 Then 1. f(x) = 16 · g(x) 2. f(x) = 17 · g(x)

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.2: Integration By Parts
Problem 41E
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The Fourier integrals of two continuous functionsf(x) and g(x) defined on R are given
by
00
f(X) = .
2л
W3
sin(wx)| dw
cos(wx) +
and
00
2n
cos(wl6x) +
w17
sin(w!®x» dv
g(x) =
| dw.
w33
Then
1.
f(x) = 16 · g(x)
2.
f(x) = 17 · g(x)
Transcribed Image Text:The Fourier integrals of two continuous functionsf(x) and g(x) defined on R are given by 00 f(X) = . 2л W3 sin(wx)| dw cos(wx) + and 00 2n cos(wl6x) + w17 sin(w!®x» dv g(x) = | dw. w33 Then 1. f(x) = 16 · g(x) 2. f(x) = 17 · g(x)
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