The good old tedious integral of 1/(1+t^4) haha.
Last edited by Paradoxica; 9 Jan 2016 at 1:24 PM.
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
Let for
Then
So we have:
To make things neater we will define from now on
We then integrate counter-clockwise about a boundary formed by to make a circular arc and get:
Now take the limit as
Now from a previously answered integral we know that:
So we then have:
Using Euler's formula we obtain:
Since the imaginary part = 0 we get:
Now equating the real part gives:
Then we just double the answer cos even function to get:
Last edited by RealiseNothing; 9 Jan 2016 at 4:25 AM.
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
2015 HSC
Mathematics 2U
2016 HSC
Advanced English, Drama, Maths 3U, Maths 4U, Music 2, Extension Music, Chemistry, Software Design & Development
Currently studying
Advanced Mathematics (Hons)/Computer Science @ UNSW (2017– )
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
2015 HSC
Mathematics 2U
2016 HSC
Advanced English, Drama, Maths 3U, Maths 4U, Music 2, Extension Music, Chemistry, Software Design & Development
Currently studying
Advanced Mathematics (Hons)/Computer Science @ UNSW (2017– )
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
Extra question:
Last edited by leehuan; 17 Jan 2016 at 11:09 PM.
Beat me to it by nine hours But my solution involved factorising out the 1/4 so basel's could be seen easily. But my main problem is that I can't get rid of the negative that appears in the series expansion for log(1-x). Here's my solution, which ignores the sign error...
WHERE DID THE MISSING SIGN GO?!?!?!
Last edited by Paradoxica; 20 Jan 2016 at 8:58 PM.
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
There are currently 1 users browsing this thread. (0 members and 1 guests)
Bookmarks