Integration by substitution.

William F · 2012-07-22 13:04:37

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?

noelevans · 2012-07-22 14:50:43

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.

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

anonimnystefy · 2012-07-22 23:57:29

Hi noelevans

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

noelevans · 2012-07-23 02:25:47

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!

anonimnystefy · 2012-07-23 02:41:44

Hi noelevans

Where are you from?

William F · 2012-07-23 02:57:21

Thanks!

William F · 2012-07-23 04:00:39

I have another similar example:

When I plug everything in I get:

Are these also the correct steps?

noelevans · 2012-07-23 04:35:22

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.

Bob · 2012-07-23 04:42:22

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

noelevans · 2012-07-23 05:22:43

Thanks bunches Bob! That will be a great help.

William F · 2012-07-23 06:28:19

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)

Bob · 2012-07-23 06:50:50

Thanks William,

I didn't know that.

Bob

anonimnystefy · 2012-07-23 06:52:49

Hi Bob

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

Math Is Fun Forum

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

Integration by substitution.

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

Re: Integration by substitution.

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

Re: Integration by substitution.

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

Re: Integration by substitution.

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

Re: Integration by substitution.

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

Re: Integration by substitution.

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

Re: Integration by substitution.

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

Re: Integration by substitution.

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

Re: Integration by substitution.

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

Re: Integration by substitution.

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

Re: Integration by substitution.

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

Re: Integration by substitution.

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

Re: Integration by substitution.

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