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#1 2012-07-22 13:04:37

William F
Member
Registered: 2012-07-03
Posts: 16

Integration by substitution.

Hi All,
    I believe this is correct but I've been known to trick myself into believing I came to a particular answer in the correct way.

Integration by substitution gives:

so....

Does this look solid?

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#2 2012-07-22 14:50:43

noelevans
Member
Registered: 2012-07-20
Posts: 236

Re: Integration by substitution.

yup! you got it right except for adding in the constant of integration.  Have you seen the tabular technique of integration by parts?  As I understand it was created by Dr. William T. Guy at the University of Texas in the 1960's or so.  Some calculus textbooks introduce this tabular technique.  It makes integration by parts a snap and useful instead of something to be avoided. smile

Last edited by noelevans (2012-07-22 14:51:35)


Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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#3 2012-07-22 23:57:29

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Integration by substitution.

Hi noelevans

The first post showed integration by substitution, not by parts.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#4 2012-07-23 02:25:47

noelevans
Member
Registered: 2012-07-20
Posts: 236

Re: Integration by substitution.

True!  I should have asked the question in a separate paragraph.  I was just trying to point out the easy way to do integration by parts in case he hadn't seen it.  It's really cool!

Dr. Guy passed away several years ago.  However I did have the pleasure of taking several courses from him.  Dr. Guy and a high school teacher R. J. Wood (Edison High in San Antonio) were my mentors.  My style of teaching was pattered after Dr. Guy's.

Top of the mornin' to you!   smile


Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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#5 2012-07-23 02:41:44

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Integration by substitution.

Hi noelevans

Where are you from?


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#6 2012-07-23 02:57:21

William F
Member
Registered: 2012-07-03
Posts: 16

Re: Integration by substitution.

Thanks!

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#7 2012-07-23 04:00:39

William F
Member
Registered: 2012-07-03
Posts: 16

Re: Integration by substitution.

I have another similar example:



When I plug everything in I get:

Are these also the correct steps?

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#8 2012-07-23 04:35:22

noelevans
Member
Registered: 2012-07-20
Posts: 236

Re: Integration by substitution.

stefy,  I'm from the US if that's what you mean.  Would you like more specifics? 

William,  Looks good to me.  When differentiating e^(ax) we get the coefficient a multiplied by e^(ax).
When integrating e^(ax) we get the coefficient 1/a instead ((1/a)e^(ax)).  Obviously if we differentiate this integral the 1/a and the a from the derivative cancel leaving e^(ax). 

So you have used substitution to derive the formula  int(e^cx dx) = (1/c)e^cx + C which can then be used to do the second integration after "pulling out" the -1/a and letting -a=c in the formula.

I gotta get LaTex going.  I wish some of these shorter posts would include the corresponding LaTex
code for a while at least for the lines with integrals.  At this point the only latex I know much about is the kind in gloves and tubes for filling cracks.  smile


Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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#9 2012-07-23 04:42:22

Bob
Administrator
Registered: 2010-06-20
Posts: 10,052

Re: Integration by substitution.

hi noelevans

If you click on the Latex you can see the code.  then all you need is square brackets math and square brackets /math around the code and you're done.

Also, there's a 'sticky' at the start of the help me section that gives loads of help.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#10 2012-07-23 05:22:43

noelevans
Member
Registered: 2012-07-20
Posts: 236

Re: Integration by substitution.

Thanks bunches Bob!  That will be a great help.  smile


Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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#11 2012-07-23 06:28:19

William F
Member
Registered: 2012-07-03
Posts: 16

Re: Integration by substitution.

Another trick that helps me with LaTex is that if you click on "quote" in the bottom right corner of a post that includes LaTex you can view exactly what code was used.

Thanks again for taking a look at this for me.

Last edited by William F (2012-07-23 06:29:35)

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#12 2012-07-23 06:50:50

Bob
Administrator
Registered: 2010-06-20
Posts: 10,052

Re: Integration by substitution.

Thanks William,

I didn't know that.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#13 2012-07-23 06:52:49

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Integration by substitution.

Hi Bob

Have you figured out the nickname K5 I gave you yet?


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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