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 Post subject: Evaluate the integral (3)
PostPosted: Thu, 23 Feb 2012 16:45:44 UTC 
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Find the indefinite integral of: e^{2x}*sin(3x) dx

Here is my attempt; apparently, I got "looped"
(ie. came back to the original question as I was going Integration by Parts...)

http://i1084.photobucket.com/albums/j40 ... MG-001.png


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 Post subject: Re: Evaluate the integral (3)
PostPosted: Thu, 23 Feb 2012 16:50:02 UTC 
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A-R-Q wrote:
Find the indefinite integral of: e^{2x}*sin(3x) dx

Here is my attempt; apparently, I got "looped"
(ie. came back to the original question as I was going Integration by Parts...)

http://i1084.photobucket.com/albums/j40 ... MG-001.png


It isn't exactly looped --- you end up with I=\text{something}+cI, where I is your integral and c\neq 1, so you have ...

_________________
\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


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 Post subject: Re: Evaluate the integral (3)
PostPosted: Fri, 24 Feb 2012 17:29:51 UTC 
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Joined: Sun, 12 Feb 2012 02:16:54 UTC
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Once you see that you have looped, you'll notice that you can just add the two, somethign liek this

integral of: e^{2x}*sin(3x) dx = something + 2/3integral of: e^{2x}*sin(3x) dx, so you can just subtract then have

integral of: e^{2x}*sin(3x) dx - 2/3integral of: e^{2x}*sin(3x) dx = something

To what the previous guy posted, :confused:


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