Symbolic Computations

Posted on 2009-11-15 20:28 By TD03 (2)

Categories:

How do I ...? with Maple (Student)

I am trying to integrate an equation that has a cos(x), sin(x), cosh(x), sinh(x). When I enter the equation in Maple and try to integrate the equation Maple just rewrites the equation without actually solving the equation. I am not sure if I have to load a specific package to complete the integration. Here is the equation:

H:= (cos(n*L)=cosh(n*L))/(sin(n*L)-sinh(n*L))

phi:=sin(n*x)-sinh(n*x)+H*(cos(n*x)-cosh(n*x))

when I write: int(phi(x), x=0..L)

maple just puts the integration symbol in front of the above equation but doesn't actually solve the integration. Does anyone know how to get Maple to actually compute this integration? Thanks, Tom

Several errors

Comment on 2009-11-15 20:53 from alec ( Maple Rating 4

2577)

You have several errors here.

First, H is an equation and in the phi definition you have some expression plus that equation multiplied by something. What does that suppose to mean?

Second, you have defined phi and then is using it as phi(x). Either you should use it as phi and not phi(x), or define is as phi :=x-> something (or as a procedure).

Third, you can't integrate equations - say int(x=x^2,x) doesn't have much sense. You need expressions instead of equations.

Alec

maybe

Comment on 2009-11-16 12:24 from PatrickT ( Maple Rating 4

552)

assuming you meant to type * instead of = in the formula for H:

H:= (cos(n*L)*cosh(n*L))/(sin(n*L)-sinh(n*L)):
phi:=x->sin(n*x)-sinh(n*x)+H*(cos(n*x)-cosh(n*x)): 
int(phi(x), x=0..L);
  1/2 (4 exp(n L) sin(n L) - 4 exp(n L) sinh(n L)

         - 2 cos(n L) sin(n L) exp(n L)

         - cos(n L) cosh(n L) exp(2 n L)

         + 2 cos(n L) sinh(n L) exp(n L) + cos(n L) cosh(n L)

         - exp(2 n L) sin(n L) + exp(2 n L) sinh(n L) - sin(n L)

         + sinh(n L) + 2 cos(n L) cosh(n L) sin(n L) exp(n L))

        exp(-n L)/((sin(n L) - sinh(n L)) n)

That works. Thanks for the

Comment on 2009-11-17 00:34 from TD03 (2)

That works. Thanks for the help