why does the integral of sin(x) from -pi to 0 in matlab 2017b gives 0 instead of -2?

I'm trying to solve a simple integral but the software gives me a wrong answer. Please help me, I'm trying to calculate a lot of integrals but this problem doesn't let me to.

[the cyclist]

Showing us the code that you believe gives an incorrect result would be helpful.

[Jorge Mera]

I mean this...my code is a little bit complicated because it's about Fourier Series but this integral is what is getting me in trouble.

[James Tursa]

What version of MATLAB? What happens when you restart MATLAB? On my machine R2016b Win64:

>> syms x
>> int(sin(x))
ans =
-cos(x)
>> int(sin(x),-pi,0)
ans =
-2

[Jorge Mera]

Thank you for answering. My MATLAB is R2017b(9.3.0.713579) for academic use. I restarted it but still doesn't work.

[Star Strider]

In a bit more detail (in R2017b):

syms x real
V1(x) = int(sin(x))
V1v = [V1(0)  V1(-pi)  V1(0)-V1(-pi)]
V2 = int(sin(x), -pi, 0) 

V1(x) =
-cos(x)

V1v =
[ -1, 1, -2]

V2 =
0

[Jorge Mera]

yes, now you see this is not working and I need it to work well. Thank you for answering.

[James Tursa]

I guess as a workaround you can do it in steps like Star.

[Jorge Mera]

yes, I thank both of you. I used the Star suggestion and it worked perfectly. Thank you again.

[per isakson]

"I need it to work well" Thus contact Service Requests

[Star Strider]

I wish I had posted that as an Answer!

Answer 1

[Greg]

I would definitely submit this to tech support. I don't even need to recall my rusty calculus to know that the results should match in R2016b and R2017b (and I've confirmed as you all have that they don't...odd).

It does look like the desired value is returned in R2017b by:

vpaintegral(sin(x),x,-pi,0)

Not sure of all the differences between int and vpaintegral, though.

[John D'Errico]

To me this feels like an error generated by the parser, but only TMW would know the true source of the error. It is definitely a bug and worth reporting as such. It might be a bugged special case inside int.

Interesting that SOME other intervals return a bug too. For example, if we add some positive integer multiple of 2*pi to the upper limit, it still returns 0.

syms x
int(sin(x),-pi,2*pi)
ans =
0

int(sin(x),-pi,12*pi)
ans =
0

(This still in R2017b.)

Surprisingly, this one does work:

int(sin(x),0,pi)
ans =
2

And it is not the fact that the lower limit was -pi.

int(sin(x),-pi,-2*pi)
ans =
-2

I tried a few similar cases, but cos(x) does not seem to bug out for any set of limits. I gave up quickly on cos though. It is also not the specific limits. so if you try a simpler kernel...

int(x,-pi,0)
ans =
-pi^2/2

There is no problem.

vpaintegral is a numerical integration tool, using a convergence tolerance. It should work much like the integral tool does, so an adaptive integration tool.