Why is the Bode plot of 1/s a straight line?
A straight line with a slope of -20dB/dec IS a curve with a slope of \$\frac{1}{\omega^2 C}\$.

Think about it.


   \$ 10*log_{10}(\frac{1}{\omega^2 C}) = \$
 \$ -10*log_{10}(\omega^2 C) = \$


 \$ -20*log_{10}(\omega) - 10*log_{10}(C)) \$


A Bode plot is in a linear dB scale in the ordinate and logarithmic scale in the abscissa.