Math Is Fun Forum

Au101

Member

Registered: 2010-12-01

Posts: 353

Definite integration (by parts)

Hi guys, I have a question regarding integration by parts over an interval. Suppose we have to integrate the following:

If we do this without limits we end up with:

My question is - when we do it between limits, should we have:

Which is how I was taught that this should be done and which gives:

Or, should we have:

Which is right and gives:

I'm confused, because i was always told to put limits in as I went - but that has given me the wrong answer. To avoid an overlong post, I shall post the exact question, with my working, in the next post. Perhaps I have made a mistake somewhere else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Definite integration (by parts)

Hi guys, so the question is:

My working - putting the limits in as I go is:

This gives the wrong answer; however, computing the antiderivative first and then simply adding the limits at the end does give the right answer.

My question, then, is this - should we add the limits in as we go as I have done here and then add them all up at the end, or save the limits until the end. One book does the former the other the latter and I have become quite confused . Thanks

Last edited by Au101 (2011-06-18 05:47:18)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Definite integration (by parts)

Hi;

In post #1

Check the boxed one please, I am not getting that.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Definite integration (by parts)

Ooops - you're right, I have made a mistake there. Let me see if fixing that will solve my problem - thanks

Last edited by Au101 (2011-06-18 06:10:43)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Definite integration (by parts)

I think it will. Let me know how you do.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Definite integration (by parts)

Oooooh thanks Bobbym - that's absolutely perfect. That has fixed it. However, I would like to confirm - does it matter whether I leave the limits out, or do it bit by bit. Will it always give the same result, or should I choose one method in preference of another?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Definite integration (by parts)

Hi;

I do it bit by bit. As long as you are careful with your arithmetic it should get the same answer.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Definite integration (by parts)

Hmmm...Okay, thanks once again Bobbym - hopefully I won't do that in my C4 exam on Monday

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Definite integration (by parts)

Hi Au101;

In all the IBP's I have ever worked on, I only had a definite integral like 3 times.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Definite integration (by parts)

Hmmm...I think it's more common with volume of revolution, but we'll see - I think it's more accuracy in general that I need to be careful with

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Definite integration (by parts)

I think you will do well. Do not worry about it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Definite integration (by parts)

Thanks a lot .

No, I'm looking forward to it, to be honest, but I know I'm liable to make silly mistakes. Had I not finished C3 with half an hour to spare I would have dropped a lot of easy marks - for example when I accidentally added, rather than subtracting, when using the quotient rule.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Definite integration (by parts)

liable to make silly mistakes.

There are no silly mistakes. Since we can not be perfect, if we do not make a math error we will surely write 3 when we mean 2.

I make about 25 - 50 of them a day. Just try limit them to fewer than what others do. That is the secret. You do not have to be perfect to win, you just have to be a little bit more accurate then the next guy.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Definite integration (by parts)

Well that's very true. Thanks for the advice.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Definite integration (by parts)

Hi Au101;

Good luck and do well. Let me know how you do.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Definite integration (by parts)

Hi Au101,

I remember a formula:

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"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Definite integration (by parts)

hi AU101

Good luck with the C4 exam.  The mark schemes allow marks for every correct step, so show all your working, neatly and clearly.  That way, even with a silly mistake, you'll only drop a mark, not the whole question.

Bob

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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

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Definite integration (by parts)

Thanks everyone, I will certainly let you know how I get on.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Definite integration (by parts)

Hey everyone - the examination this morning was pretty difficult. In fact I made a big mistake on an IBP question and was only able to fix it right at the very end - I knew I'd done something wrong, when I got a negative area . It was fairly enjoyable, though, and whilst there were a lot of tricky parts and I'm sure I lost quite a few marks, I think it went rather well, overall, so I'm feeling quite happy about it

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Definite integration (by parts)

hi Au101,

Thanks for letting us know.  Fingers crossed for results day. 

Is that it for this block of exams?

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Definite integration (by parts)

H Au101;

Congratulations! Sounds like you did well.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Definite integration (by parts)

Hi guys - Yeah C4 was my last exam for this year, so I'm hoping to use my holiday to get to grips with some more interesting stuff . Thanks bobbym - I certainly enjoyed it, I don't know if I did well or not, but I was happy with what I managed so I suppose I just have to wait and see

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Definite integration (by parts)

The only good thing about tests is when they are over. Also test is a four letter word.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.