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#1 2014-08-20 12:35:44

Au101
Member
Registered: 2010-12-01
Posts: 353

Proof Check

The last question on integration by substitution in my books asks for a proof. I think I've got it, but obviously the proof's not given in the back, so I could be talking absolute nonsense. I was wondering, therefore, if someone could give it a look over and tell me if I'm right in my approach.

Here's the question:

My approach was as follows:

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#2 2014-08-20 19:38:56

Bob
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Registered: 2010-06-20
Posts: 10,058

Re: Proof Check

hi Au101

That looks good to me.  smile

Well done.

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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#3 2014-08-21 10:54:39

Au101
Member
Registered: 2010-12-01
Posts: 353

Re: Proof Check

Thanks! smile

There's actually a second part of this question and, sadly, I'm totally stuck on that too!!

I reckon this could be done quite easily with integration by parts, but in the textbook this is the last question in an exercise on integration by substitution. Integration by parts is actually the next subsection, so I'm wondering if there's another way?

I don't even know where to start with this. I tried using what I just proved, but it doesn't seem to help - at least not in the very first place. I imagine I'll be able to use it after finding the first integral, but I can't seem to use it to do anything useful to the first integral, since

There's nothing that I can think to substitute.

I did do some algebra to get:

But that does nothing about the x it's multiplied by.

Does anybody have any ideas?

Last edited by Au101 (2014-08-21 10:55:39)

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#4 2014-08-21 19:17:02

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

Re: Proof Check

hi Au101,

Looks like integration by parts to me.  I cannot see how else you can deal with the mix of 'x' and trig.  Try it that way and see what happens.

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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#5 2014-08-23 04:16:16

Au101
Member
Registered: 2010-12-01
Posts: 353

Re: Proof Check

Hi bob bundy, suppose we reason thus, based on what we proved before:

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#6 2014-08-23 04:19:23

Au101
Member
Registered: 2010-12-01
Posts: 353

Re: Proof Check

Then:

Last edited by Au101 (2014-08-23 04:19:41)

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#7 2014-08-23 04:22:59

Au101
Member
Registered: 2010-12-01
Posts: 353

Re: Proof Check

Oh N.B. for anyone who didn't follow:

I believe. Hence step 3.

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