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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: acinod on May 19, 2011, 05:15:47 pm

Title: Acinod's Question Thread
Post by: acinod on May 19, 2011, 05:15:47 pm
Without using integration by parts or recognition and showing full working, integrate the following:

Let u=tan(x/2), -pi<x<pi. Find sin(x) and cos(x) as a rational expression of u only without using any trigonometry notations.
Title: Re: Acinod's Question Thread
Post by: dcc on May 19, 2011, 05:44:04 pm
Code: (Mathematica Output) [Select]
In[8]:= Integrate[Log[x], x]
Out[8]= -x + x Log[x]

In[9]:= Integrate[x*Cos[x], x]
Out[9]= Cos[x] + x Sin[x]
Title: Re: Acinod's Question Thread
Post by: acinod on May 19, 2011, 05:45:44 pm
Quote from: dcc on May 19, 2011, 05:44:04 pm
Code: (Mathematica Output) [Select]
In[8]:= Integrate[Log[x], x]
Out[8]= -x + x Log[x]

In[9]:= Integrate[x*Cos[x], x]
Out[9]= Cos[x] + x Sin[x]

Oops sorry I forgot to mention, full working required.
Title: Re: Acinod's Question Thread
Post by: dcc on May 19, 2011, 05:46:10 pm
The full working was provided.


(http://i.imgur.com/TK6sY.jpg)
Title: Re: Acinod's Question Thread
Post by: acinod on May 19, 2011, 06:54:01 pm
Quote from: dcc on May 19, 2011, 05:46:10 pm
The full working was provided.

Wow after staring at the working for a couple of minutes, I finally understood what you did there. Actually I'm still a bit confused but I get the general idea.
Is there another way to do this? Like using only the knowledge learnt in the Year 12 course?
Title: Re: Acinod's Question Thread
Post by: dcc on May 19, 2011, 07:13:56 pm
Back in my day, this was part of the Year 12 course.