Problem with integrating Sin to Cos

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Good day.
I am trying to integrate the following equation but Matlab seems to not integrate Sin to Cos?
Not sure if the error is in my code.
ode = (2/pi) * (int(sin(n*x), 0, pi/2))
ode = (4*sin((n*pi)/4)^2)/(n*pi)
Any help will be appreciated.
Thank you
  2 Comments
Jan
Jan on 3 Apr 2021
Do you get an error message? Then please share it,
Ruwan Badenhorst
Ruwan Badenhorst on 4 Apr 2021
Hi Jan. No error message.
The issue I'm having is that sin will not integrate to cos with the limits "0" and "pi/2"
The answer still shows it is sin, but sin integrated is -cos

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Accepted Answer

Walter Roberson
Walter Roberson on 4 Apr 2021
syms n x
Pi = sym(pi);
ode = (2/Pi) * (int(sin(n*x), x))
ode = 
result1 = simplify(subs(ode,x,Pi/2) - subs(ode,x,0))
result1 = 
result2 = (2/Pi) * (int(sin(n*x), x, 0, Pi/2))
result2 = 
result1 - result2
ans = 
simplify(ans)
ans = 
0
The result you are seeing is not wrong: it is the same result, expressed differently due to an identity.
  1 Comment
Ruwan Badenhorst
Ruwan Badenhorst on 4 Apr 2021
Thank you very much Walter. You deserve a Bells!
I see where I made my error.

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More Answers (1)

Paul
Paul on 4 Apr 2021
If you just want ode in terms of cos()
>> ode = int(sin(n*x),x,0,pi/2)
ode =
(2*sin((pi*n)/4)^2)/n
>> rewrite(ode,'cos')
ans =
-(2*(cos((pi*n)/4)^2 - 1))/n
The "by hand" solutions is:
>> sol=1/n*(-cos(n*pi/2) + cos(0*n))
sol =
-(cos((pi*n)/2) - 1)/n
Show the two solutions are equal:
>> simplify(ode-sol)
ans =
0
Wrangling ode into the form of sol takes a few steps. Perhaps someone else can do it easier:
>> simplify(combine(rewrite(ode,'cos')))
ans =
-(cos((pi*n)/2) - 1)/n

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