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Integration Tutor: determine u-sub

Posted on 2008-12-03 21:20 By finstabelized (1)
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I'm a brand new user. 

Maple 12, Windows Vista, Integration Tutor.

When viewing the steps in the solution, Maple does it's own u-subs ("change of variable").  Is there any way to see what it is setting "u=?"?

It's very difficult to follow the steps when I can't tell what it's subbing out.

Also, within the same tutor, it doesn't seem to like to intigrate to infinity.  It tells me "...infinity should be a number."  ! ? ! ?

 

Thank you in advance.

Jim Z

‹ confused about a differentiation differentiability test ›
Robert Israel's picture

Integration tutor

Comment on 2008-12-03 22:09 from Robert Israel (Maple Rating 4 1554)

I don't know if it's possible to see what substitution is being made within the IntegrationTutor, but in the worksheet itself you can do something like this:

> with(Student[Calculus1]):
  J := Int(sin(exp(x)) * exp(x), x);

= Int(sin(exp(x))*exp(x), x)

> R := Hint(J);

R := [change, u = exp(x), u]

> J := Rule[R](J);

= Int(sin(exp(x))*exp(x), x) = Int(sin(u), u)

Moreover, in the worksheet there's no problem with infinity as an endpoint.

gkokovidis's picture

Integration Tutor: determine u-sub

Comment on 2008-12-03 22:14 from gkokovidis (Maple Rating 4 700)

The integration tutor will not show you this.  And even if it did, it might not be what you would have chosen if you did it by hand step by step.  My advice would be to use it as a verification of your answer, or as an aid, but do not use it to guide you step by step.  Working through the problems in a standard calculus text by hand is the best way to learn how to do this, and ultimately to gain experience and insight as to how to choose the u-substitution variable on your own.  As an example, you might try the integration tutuor with this problem:

sqrt(2*x-1)

When asked for the next step, it chooses u^2 after substitution. This is correct, but there are steps ommited.   When doing this by hand, my choice would be to let u=2*x-1, and then du=2dx.  At the end, you will get the same answer.  The only thing I am pointing out is that your choice of substitution variables might not be Maple's choice.  Either way, practice by hand with many many problems is the best way to learn.

 

Regards,
Georgios Kokovidis
Dräger Medical

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