Inconsistency Between Analysis and Simulation Results of Fourier Transform of a Sinc Function
I have recently answered a related question.
What happens is that MATLAB fft is calculating a sum in the sampled points, the integral would be approximated with a (Riemann) sum.
$$ \int_{0}^{T} f(x)dx \approx \sum_{k=0}^{N-1} x(k \Delta t) \Delta t$$
The $\Delta t=0.01$ factor matches the two results.