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## #1 2015-08-27 22:05:24

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

### questions from integration

Q.1.

find a,b,c,d and f.

friendship is tan 90°.

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## #2 2015-08-28 09:23:34

White_Owl
Member
Registered: 2010-03-03
Posts: 106

### Re: questions from integration

Integrate the left side. Simplify it. The result should be equal to the expression on the right.
Or backward - differentiate the right side, the result should be equal to the expression under the integral.

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## #3 2015-08-28 19:08:28

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: questions from integration

Hi;

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.

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## #4 2015-08-28 19:15:53

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

### Re: questions from integration

I tried integrating left or differentiating right but it became lengthy.
bobbym, what's EM method?

friendship is tan 90°.

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## #5 2015-08-28 20:21:09

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: questions from integration

Hi;

That is an acronym for Experimental Mathematics.

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.

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## #6 2015-08-28 21:07:29

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,210
Website

### Re: questions from integration

Let u = sin(x) and express sin(3x) in terms of sin.

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## #7 2015-08-30 22:59:43

bob bundy
Registered: 2010-06-20
Posts: 8,398

### Re: questions from integration

My earlier suggestion didn't, work, sorry.

But this does.

Start with the right hand side and differentiate chiefly using the product rule.

Use zetafunc`s suggestion to express sin(3x) in terms of sin(x) and sin cubed.

Now make the left hand side look like the right hand side.

You can quickly determine a to start off the sin cubed term and b to avoid any sin squared (remember sin squared + cos squared).

Then fix c to finalise the sin3x and sin x terms.

Then d and f allow you to tidy up the rest.

Bob

Last edited by bob bundy (2015-08-31 04:08:42)

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

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## #8 2015-09-01 14:01:06

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

### Re: questions from integration

yes I solved it now. Thanks.

here comes another question:-

friendship is tan 90°.

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## #9 2015-09-01 15:14:51

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: questions from integration

Was post #3 the official 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.

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## #10 2015-09-02 09:53:40

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,210
Website

### Re: questions from integration

niharika_kumar wrote:

yes I solved it now. Thanks.

here comes another question:-

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## #11 2015-09-02 19:33:51

bob bundy
Registered: 2010-06-20
Posts: 8,398

### Re: questions from integration

hi zetafunc,

Beautiful solution!  And nicely explained.

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

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## #12 2015-09-03 13:19:02

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

### Re: questions from integration

thanks. It was really very well explained.
well what are the things that should come in our mind for making substitution when we encounter such problems?

friendship is tan 90°.

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## #13 2015-09-03 21:16:56

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,210
Website

### Re: questions from integration

Normally with these types of problems, in which you've got a function nested within another function (e.g. log(sin(x)), e^(tan(x)), arctan(sec(x) + cos(x))), what they expect you to do is to make the most obvious substitution -- in this case, whatever the function inside arctan() was.

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