If f(x) represented by Fourier integral $f(x)=\int_0^{\infty} [A(ω) cos~ω x + B(ω) sin~ω x]dω $then A(ω) is defined as

Question

If f(x) represented by Fourier integral $f(x)=\int_0^{\infty} [A(ω) cos~ω x + B(ω) sin~ω x]dω $then A(ω) is defined as

TuteeHUB · Accepted Answer

​​$​\frac{1}{\pi}\int_{-\infty}^{\infty} f(v) ~sin~\omega v ~dv$

TuteeHUB · Answer

​$\frac{1}{\pi}\int_{-\infty}^{\infty} f(v) ~cos~\omega v ~dv$

TuteeHUB · Answer

$​\int_{-\infty}^{\infty} f(\omega) ~cos~\omega v ~dv$

TuteeHUB · Answer

$​\int_{-\infty}^{\infty} f(\omega) ~sin~\omega v ~dv$

1.	If f(x) represented by Fourier integral \(f(x)=\int_0^{\infty} [A(ω) cos~ω x + B(ω) sin~ω x]dω \)then A(ω) is defined as
A.	\(\frac{1}{\pi}\int_{-\infty}^{\infty} f(v) ~cos~\omega v ~dv\)
B.	\(\frac{1}{\pi}\int_{-\infty}^{\infty} f(v) ~sin~\omega v ~dv\)
C.	\(\int_{-\infty}^{\infty} f(\omega) ~cos~\omega v ~dv\)
D.	\(\int_{-\infty}^{\infty} f(\omega) ~sin~\omega v ~dv\)
Answer» B. \(\frac{1}{\pi}\int_{-\infty}^{\infty} f(v) ~sin~\omega v ~dv\)

If f(x) represented by Fourier integral \(f(x)=\int_0^{\infty} [A(ω) cos~ω x + B(ω) sin~ω x]dω \)then A(ω) is defined as