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Math Help - Definite integral

  1. #1
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    Definite integral

    Hi, I have a very basic question to ask. The Integral is

    (P^-1) dt from 0 to t. Can I rewirte it as lnP(at t) - lnP(at 0)? Where P is pressure and is varying with time.
    Please help?
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  2. #2
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    Quote Originally Posted by lalleykhan View Post
    Hi, I have a very basic question to ask. The Integral is

    (P^-1) dt from 0 to t. Can I rewirte it as lnP(at t) - lnP(at 0)? Where P is pressure and is varying with time.
    Please help?
    Dear lalleykhan,

    If you had t instead of p you could write it as lnt. That is,

    \int^{t_{1}}_{t_{2}}{\frac{1}{t}}dt=\ln{t_{1}}-\ln{t_{2}}

    But in this case you cannot do so. But do you know the relation between P and t? If so we could try to solve the integral.
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  3. #3
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    Thanks Sudharka,

    The problem is that I have discrete values of pressure at different time instances but I do not have a function which can relate P to t. Can you suggest what can I do in this case?
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  4. #4
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    Quote Originally Posted by lalleykhan View Post
    Thanks Sudharka,

    The problem is that I have discrete values of pressure at different time instances but I do not have a function which can relate P to t. Can you suggest what can I do in this case?
    Dear lalleykhan,

    Ok. Then you can draw a graph between \frac{1}{p}~vs.~t. That is your y axis must be 1/p and your x axis must be t. So if you find the area bounded by this curve and the x axis from 0 to t you can get \int^{t}_{0}{\frac{1}{p}dt}

    Hope this will help you.
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