Rogawski Integration by Parts Conception Problem

[Integrate]

I am trying to teach myself calculus and have been going through problems and this one is just too high minded for me.

View attachment 19770

First off its just confusing that they use Two v's.

When I do part a it just amount to some simple canceling with the C's

but with part b I just don't know how big V plays a part.


What is the point of the exercise?

 

[Deleted member 4993]

I am trying to teach myself calculus and have been going through problems and this one is just too high minded for me.

View attachment 19770

First off its just confusing that they use Two v's.

When I do part a it just amount to some simple canceling with the C's

but with part b I just don't know how big V plays a part.

What is the point of the exercise?

Your attachment is not displaying on our screens. Fix it.

You have said that you have done part a. Please include your work of part a.

 

[Integrate]

Hopefully this works.

 

[Deleted member 4993]

I am trying to teach myself calculus and have been going through problems and this one is just too high minded for me.

View attachment 19770

First off its just confusing that they use Two v's.

When I do part a it just amount to some simple canceling with the C's

but with part b I just don't know how big V plays a part.


What is the point of the exercise?

In my opinion, it is showing that while integrating by parts - you have choice of functions (that will give the same result). A clever choice of V(x) that is shown for part (b) will require considerably less work (yielding same result as the choice of "not-so-clever" V(x)).

However, my suggestion is that unless that "clever-choice" jumps out at you - do not spend time hunting for it.Most of the time you get the same credit with "clever answer" and "not-so-clever answer".

 

[Integrate]

In my opinion, it is showing that while integrating by parts - you have choice of functions (that will give the same result). A clever choice of V(x) that is shown for part (b) will require considerably less work (yielding same result as the choice of "not-so-clever" V(x)).

However, my suggestion is that unless that "clever-choice" jumps out at you - do not spend time hunting for it.Most of the time you get the same credit with "clever answer" and "not-so-clever answer".

Thank you. I was thinking the same but sometimes there seems to be so much notation and jargon that I misinterpret things. Thank you greatly.

 

[HallsofIvy]

As far as the "two v's" is concerned, they specifically tell you that "V'= v". That is, V is defined as the "anti-derivative" of the function v.

 

[Integrate]

Thank you