Integration problem

Cameron.S

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May 23, 2020
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Struggling to integrate the equation, pretty sure it can be done by integrating by parts but not sure how
 

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Dr.Peterson

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You should be able to immediately integrate \(\displaystyle e^{-\frac{t}{T}}\). That doesn't require parts, just a simple substitution, if that.

What you might want to do is first just to check the answer they give; in fact, that is really enough to answer the question. Differentiate the given function \(\displaystyle \phi(t)\), and show that (a) the derivative is what you were given, and (b) \(\displaystyle \phi(0) = 0\).
 

Cameron.S

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Thanks for the help, tried this method and I’m missing the 1 inside the brackets. Not sure how this can be found?
 

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Subhotosh Khan

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Thanks for the help, tried this method and I’m missing the 1 inside the brackets. Not sure how this can be found?
Where did C go in your final step?
 

Dr.Peterson

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You'll have to use the fact that \(\displaystyle \phi(0) = 0\) to determine the value of C. You can't just call it 0, as you have.
 
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