Problem Integrating sin(2*x)

>> syms x >> f=sin(2*x)

f =

sin(2*x)

>> int(f)

ans =

sin(x)^2

>>

I am sure it is wrong because it should be -1/2+sin(x)^2

Answer 1

[Paul]

The integral is:

sin(x)^2 + C

but Matlab just doesn't show the constant. How do you get the -1/2? Because if you differentiate the integral (sin(x)^2 + C) you get:

2*sin(x)*cos(x) = sin(2*x)

And the constant differentiated gives 0 since it doesnt depend on x.

[Ricardo]

I got the 1/2 integrating on my notebook, following my integration formulas i got: (-1/2)*cos(2x) "but when I saw it was different from matlab´s answer i tried to fit on it by (-1/2)*cos(2x)=(-1/2)*(cos^2(x)-sin^2(x)) =(-1/2)*(1-sin^2(x)-sin^2(x)) =(-1/2)+sin^2(x)

[Paul]

Yes, (-1/2)*cos(2x) is also correct. The constant just doesn't matter in the integral because it could be anything, see http://en.wikipedia.org/wiki/Constant_of_integration. Because if you use the integral to calculate the area under the graph of f you will get the same result with any constant. In this case you will get the same result using sin(x)^2 or (-1/2)*cos(2x).

[Ricardo]

All right, Thanks!!

[Gustavo Leal]

sin(pi)^2 != -cos (2pi)/2 ,for example, something its wrong with this function at MATLab