int is the command function for calculating integrals. In the Matlab command window, enter the program in the format:
int(f,x,[a,b])
Press Enter to output the result. Where
int(f,x): The function f calculates the indefinite integral with respect to the symbolic variable x;
int(f,x,[a,b]): The function f calculates the definite integral with respect to the symbolic variable x over the interval [a,b].
Example 1: Calculate the indefinite integral of f(x)=2sin(3x+1).
Solution: Enter the following in the command window:
>> syms x;
>> f=3*sin(3*x+1);
>> int(f,x)
ans =-cos(3*x + 1)+C
Note: When calculating the indefinite integral, the result obtained by Matlab is an antiderivative, and the indefinite integral represents the entire set of antiderivatives, so we need to consider the “+C” in the result.
Example 2: Given f(x)=2e^2x, calculate the definite integral of f(x) over [0,1].
Solution: Enter the following in the command window:
>> syms x;
>> f=2*exp(2*x);
>> int(f,[0,1])
ans =exp(2) – 1
Example 3: Given f(x)=xcosx, calculate the definite integral of f(x) over [0,π].
Solution: Enter the following in the command window:
>> syms x;
>> f=x*cos(x);
>> int(f,[0,pi]) 
: In MATLAB, “π” is represented as “pi”
ans =-2
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