Could someone help me to understand why Mathematica seems not see that (sin(nPi)=0) ?
In[2]:= Integrate[t Sin[ 2 n t], {t, 0, \[Pi]}, Assumptions -> Element[n, Integers] && n > 0]
Out[2]= (-2 n \[Pi] Cos[2 n \[Pi]] + Sin[2 n \[Pi]])/(4 n^2)
Mathematica should “see” that Sin[n Pi] with n natural is always null, and thus give right the answer -Pi/(2*n) (n = 1..infinite)
What happens, what did I do wrong?
Thx to you.
Hi,
try
Assuming[m \[Element] Integers && m > 0, Integrate[t Sin[2 m t], {t, 0, Pi}]]
It also works with n, but I usually try to avoid n because there is a function N and sometimes that can be confusing.
Alternatively, you can first integrate and then simplify using assumptions:
FullSimplify[Integrate[t Sin[2 n t], {t, 0, Pi}], Assumptions -> n \[Element] Integers && n > 0]
Cheers,
Marco
Hi,
try
Assuming[m [Element] Integers && m > 0, Integrate[t Sin[2 m t], {t, 0, Pi}]]
It also works with n, but I usually try to avoid n because there is a function N and sometimes that can be confusing.
Cheers,
Marco
It’s magic and you’re great, many thx
Milos.
PS : I read your post with Outlook and thus, n apparates as dollar-n-dollar. Sorry, but I’m still curious abour the perhaps dysfunction of (Elements->..) ?
Hi Milos,
it’s not really magic -just syntax.
PS : I read your post with Outlook and thus, n apparates as
dollar-n-dollar. Sorry, but I’m still curious abour the perhaps
dysfunction of (Elements->..) ?
I don’t use Outlook, but the n comes from the markdown syntax that the community uses. It’s a bit like Latex and I instinctively use it for formatting text. If you read the post in a browser it will not show up.
Regarding the Element function I think it works just fine.
This function shows you what is going on in my line of code:
Assuming[m \[Element] Integers && m > 0, Integrate[t Sin[2 m t], {t, 0, Pi}]] // HoldForm // TreeForm
This here is what your code does:
That should help you to understand what is going on.
Cheers,
Marco
