# Math Help - Definite integral

1. ## 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?

2. Originally Posted by lalleykhan
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.

3. 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?

4. Originally Posted by lalleykhan
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.