For a function g(t), it is given that \(\mathop \smallint \limits_{ - \infty }^{ + \infty } g\left( t \right){e^{ - j\omega t}}dt = \omega {e^{ - 2{\omega ^2}}}\) for any real value \(\omega \).If, \(y\left( t \right) = \mathop \smallint \limits_{ - \infty }^t g\left( \tau \right)d\tau \), then \(\mathop \smallint \limits_{ - \infty }^\infty y\left( t \right)dt\) is:

For a function g(t), it is given that \(\mathop \smallint \limits_{ -

1.	For a function g(t), it is given that \(\mathop \smallint \limits_{ - \infty }^{ + \infty } g\left( t \right){e^{ - j\omega t}}dt = \omega {e^{ - 2{\omega ^2}}}\) for any real value \(\omega \).If, \(y\left( t \right) = \mathop \smallint \limits_{ - \infty }^t g\left( \tau \right)d\tau \), then \(\mathop \smallint \limits_{ - \infty }^\infty y\left( t \right)dt\) is:
A.	0
B.	\(-j\)
C.	\(-\frac{j}{2}\)
D.	\(\frac{j}{2}\)
Answer» C. \(-\frac{j}{2}\)