I woud like to have some help in using Maple to solve some complicated integrals.Specificaly, I would like to take the help of maple in differentiating an integral w.r.t. a parameter.
First, I will start with an integral for which Maple gives a solution. Let me first start with the assumptions :
Then, I will define my first function
If we integrate,
Is there any way of completely removing the assumption sign for the parameters a and b? I don't need any reminders that I am asuming values (correct for my physical problem).
Now, I will define my next function
Integrating this function, we get
Maple does not give a solution.
I have, on my own, shown that the solution is :
I would like know how I can program Maple to get the same solution.
The first step in obtaining a soution is to differentiate the integral I2 with respect to b.
I would ike to show that the solution ies in ing the differential equation (the integral I2 is denoted as I) :
I am new to Maple. Can I get some help here? Actually, I am interested in solving more complicated integrals. When I know how I can program in Maple, I can move on to these more complicated integrals.
When I first tried the integration w.r.t. the parameter b (with the assumptions), I could not get the solution shown above. Should I take away the assumptions (which is only logical when differentiang wrt it). Actually, I got the solution above only after I started formulating this question for this newsgroup. The reason why I started with the assumption is that I did not want any compex solutions (which I got for another problem). So, the question is really if it is possibe to relax the assumptions just for the sake of differentiating the integral.
On a side note, when verifying the solutions, I could not succeed in using evalf with pi. For example,
does not give a numerical value.
Is there some way of forcing Maple to return a numerical value with a desired precision?
I will appreciate any help that I can get.