Build in FFT compared to FT Equation

How can I compare the built in FFT in Matlab to the actual Fourier Transform Equation?

The first graph displays the frequency. Second graph is using the built in FFT in Matlab. Third graph should plot the signal using the Fourier Transform Equation.

fs = 10000;                 %Sampling Frequency
ts = 1/fs;                  %Sampling Time
N = 10000;                  %Length of Signal
n = (0:N-1)*ts;             %Time
X = 100;                    %Frequency of Signal

xsig = sin(2*pi*X*n);
subplot(3,1,1)
plot(n,xsig);
grid on;
axis([0 0.1 -2 +2])
xlabel('Time');
ylabel('Amplitude');
title('Frequency');

subplot(3,1,2)
plot(abs(fft(xsig)))
title('Time');
axis([0 500 0 6000]);
xlabel('Frequency');
ylabel('Magnitude');

for k = 1:N

      X(k) = (1/N)*sum(x(n) * exp(-1i*2*pi*(k-1)*(n-1)/N)' );

end

subplot(3,1,2)
plot(abs(X(k))
title('Time');

xlabel('Frequency');
ylabel('Magnitude');

Answer 1

[Walter Roberson]

You will need to either compute the transform elsewhere and implement it, or else use the Symbolic Toolbox to calculate the transform, and then substitute specific numeric data into that in order to plot it.

http://www.mathworks.com/help/symbolic/fourier.html