How to do integration in MATLAB?

MATLAB 2013.b supports direct integration.
It supports both definite and indefinite integrals.
However, if complicated functions are given you will see a message in the command window stating that the explicit integral could not be found. For definite integrals, the approximate result can be obtained by using 'double' function for the result of integration. If the integration results in a singular result, this won't work.

Format:
syms x;
y=int(sin(x),x);

The first line is for declaring 'x' as a symbolic variable.
This will result in
y=-cos(x)

If you are using definite integral,if you enter double(y), it will return the approximate value of the integration.
Try some examples on your own.

MATLAB code for n-channel enhancement MOSFET with early effect

Enhancement mode MOSFET is influenced by early effect that arises in short channel devices. Since we are dealing with 180nm technology the devices are prone to short channel effects. This channel length modulation introduces an additional term in the MOSFET equation. It’s represented as ‘λ’ but is different from the device parameter used for expressing sizes of transistor parts. It’s the inverse of early voltage. The implication can be understood by observing the output characteristics. The curve influence by channel length modulation will develop a slope corresponding to the early voltage in the saturation region of the output characteristic of the NMOSFET. This video gives a better explanation to the working of MOSFET and guides you through the implementation of code and interpretation of graphs.

MATLAB CODE 

%n-channel enhancement mode MOSFET output characteristics

clear all;

%kn=un*cox = 100 microA/Volts

kn=1e-4;

%Let W/L= 2

W=360*(10^(-9));

L=180*(10^(-9));

beta=kn*W/L;

%Vth is the threshold voltage

Vth=1;

%lambda is the inverse of early voltage in voltage inverse

lambda=1/1000;

%Sweep drain to source voltge from 0 to 10V

vds=0:0.5:10;

%Ask the user to enter gate to source voltage

vgs=input('ENTER THE Vgs in volts');

%Estimate length of the array

m=length(vds);

for i=1:m

if vgs < Vth

current(1,i)=0;

current1(1,i)=0;

elseif vds(i) >= (vgs - Vth)

current(1,i)=0.5* beta * ((vgs - Vth)^2)*(1+lambda*vds(i));

current1(1,i)=0.5* beta * ((vgs - Vth)^2);

elseif vds(i) < (vgs - Vth)

current(1,i)= beta*((vgs-Vth)*vds(i) - 0.5*(vds(i)^2))*(1+lambda*vds(i));

current1(1,i)=beta*((vgs-Vth)*vds(i) - 0.5*(vds(i)^2));

end

end

plot(vds,current(1,:),'b',vds,current1(1,:),'r')

xlabel('Vds, V')

ylabel('Drain Current,A')

title('I-V Characteristics of a MOSFET')

OUTPUT CHARACTERISTICS

In this graph, the early voltage is 200V. So the effect is higher than the case following this. The output characteristics have been highly modified with the help og graph editor in MATLAB to help viewers explore them.

 In this graph the early voltage is 1000 V. Therefore, the curve is not so sloppy. This is the original appearance of the output curve without any modification. In other words, this curve obeys the code!

MATLAB code for n-channel MOSFET output characteristics

MOSFET is the most widely used semiconductor device in the present era. It's important to understand the working of MOSFET and graphical explanation helps in obtaining a fairly good idea on MOSFETs. Here is the MATLAB code for plotting the output characteristics of  an n-channel MOSFET. The graph is also given below. Use this video for VIDEO and AUDIO guidance and better explanation.

180 nm technology is assumed since it is the latest in use.
Early effect is not considered.

MATLAB code

%n-channel enhancement mode MOSFET output characteristics 

clear all;

%kn=un*cox = 100 microA/Volts

kn=1e-4;

%Let W/L= 2

W=360*(10^(-9));

L=180*(10^(-9));

beta=kn*W/L;

%Vth is the threshold voltage

Vth=1;

%Sweep drain to source voltge from 0 to 10V

vds=0:0.5:10;

%Ask the user to enter gate to source voltage

vgs=input('ENTER THE Vgs in volts');

%Estimate length of the array

m=length(vds);

for i=1:m

if vgs < Vth

current(1,i)=0;

elseif vds(i) >= (vgs - Vth)

current(1,i)=0.5* beta * (vgs - Vth)^2;

elseif vds(i) < (vgs - Vth)

current(1,i)= beta*((vgs-Vth)*vds(i) - 0.5*(vds(i)^2));

end

end

plot(vds,current(1,:),'b')

xlabel('Vds, V')

ylabel('Drain Current,A')

title('I-V Characteristics of a MOSFET')

OUTPUT CHARACTERISTICS

Vgs=4V

MATLAB PROGRAM FOR AUTO-CORRELATION (DIGITAL SIGNAL PROCESSIING)

clear all;
x=input('enter the sequence x=');
N=length(x);
y=x;
z=x;
for i=1:N-1
    for i=N-1:-1:1
        x(i+1)=x(i);
    end
    x(1)=0;
    z=[z; x];
end;
m=[z]*[y'];
m=m/N
stem(m);
title('auto-correlation');
xlabel('time index');
ylabel('amplitude');