Problem with integrating Sin to Cos

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

[Jan]

Do you get an error message? Then please share it,

[Ruwan Badenhorst]

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

Answer 1

[Walter Roberson]

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.

[Ruwan Badenhorst]

Thank you very much Walter. You deserve a Bells!

I see where I made my error.

Answer 2

[Paul]

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