Wrong integration trigonometric function

Hi all,

I was getting wrong answers for the integeral of the next expression,

   >> syms x
    >> f(x)=sin(x)+2*cos(x)
    f(x) =
    2*cos(x) + sin(x)
    >> F=int(f(x))

The result integral came as:

F =

    -2*cos(x/2)*(cos(x/2) - 2*sin(x/2))

So I tried to operate each term separately to get the right answer, which is different than the first one.

 >> F2=int(sin(x))+int(2*cos(x))
 
 F2 =
 
2*sin(x) - cos(x)

I tried the web version of matlab to check possible bugs within the version I'm using, but I found the same error anyway.

Maybe I am doing it wrong. Please help.

Answer 1

[Steven Lord]

syms x
f=sin(x)+2*cos(x)

f = 

F=int(f)

F = 

F2=int(sin(x))+int(2*cos(x))

F2 = 

You have different results but that doesn't necessarily mean that either is wrong.

simplify(F-F2)

ans = 

The difference between the two solutions is a constant and this is okay due to the constant of integration. But let's check that if we differentiate the results from the three int calls we get back to the original expression.

isAlways(diff(F, x) == f)

ans = logical
   1

isAlways(diff(F2, x) == f)

ans = logical
   1

Yes in both cases. So you have two different but both correct answers.

[Diego Orellana]

Thanks a lot.