Basic Integration from negative infinity to a variable

Hello all!

I have just started using MATLAB, so do bear with me.

I'm trying to intergerate the following function: exp(-x)*cos(2*pi*t) from negative infinity to t

So what I will is first declare the functionas fun1: fun1 = @(x)exp(-x)*cos(2*pi*t)

After which, I should do this: syms t (not sure what this does too, can anyone explain?)

Then I will do this where r is my output: r = integral (fun1,-Inf,t)

However it givees me an error: Error using integral (line 85)

A and B must be floating-point scalars.

Not sure what I did wrong, can anyone help? Thanks :)

[David Goodmanson]

Hi HW

Before you get to the code, I'm assuming you do mean exp(-x)*cos(2*pi*t) rather than exp(-x)*cos(2*pi*x). Then cos(2*pi*t) can be factored out of the integral since it's independent of x. That leaves the integral of exp(-x) from -infinity to t. But that integral is infinite, because the argument of the exponent is increasing as x --> -infinity.

Answer 1

[Surya Talluri]

I understand that your lower limit is -Inf, it makes e^(-x) tends to Inf.

In MATLAB, you can create symbolic math variables using “syms” function and use “int” function to integrate the symbolic functions created.

syms t 
fun1 = @(x)exp(-x)*cos(2*pi*t); 
 
r = int(fun1,-Inf,t) 
 
r = 
  
Inf*(2*cos(pi*t)^2 - 1) 

You can refer to following documentation for further understanding of Symbolic Math Toolbox:

• syms - https://www.mathworks.com/help/symbolic/syms.html
• int - https://www.mathworks.com/help/symbolic/int.html