Math Is Fun Forum

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

integration

Q.

This is what I did and could not proceed further:-

first I multiplied numerator and denominator with 2
and got

assuming (3x^2+2x+1)=t and differentiating it,

I got

now I want to know what I can do after this.

Last edited by niharika_kumar (2014-05-29 04:46:42)

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zetafunc

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Re: integration

niharika_kumar

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From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: integration

oh yes. thanks.

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niharika_kumar

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From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: integration

And what about this question:-

Last edited by niharika_kumar (2014-05-29 15:22:23)

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Bob

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Posts: 10,623

Re: integration

hi

You can substitute u = root(7x+9)  The changed integral has powers of u on the numerator so it can be done. 

Bob

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You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
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niharika_kumar

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From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: integration

can you explain a little more please.
I have just started studying and doing integration 2 days before, so am just a novice right now.

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Bob

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Re: integration

When you use substitution, you need to change every instance of 'x' into 'u' instead.

re-arrange this to get 3x + 5

(if there were definite integral values, change those too)

Finally, differentiate implicitly **:

Now we are ready to make all the substitutions:

Because the denominator now cancels, the integral is one you can do.  Afterwards substitute back the x expression to get the final answer.

Bob

** Purists may be unhappy about the way I have written this.  Alternatively you could write

Then

In the end it comes to the same thing.  The test of any method of integration is "Does it work?" ie.  If you differentiate what you've got, do you get back to the question?

Last edited by Bob (2014-05-31 00:07:10)

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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

niharika_kumar

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From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: integration

thanks bob, it really helped.:)

Calculus is looking interesting to me.It's fun.

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Bob

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Re: integration

It's fun.

Well, you're in the right place then! 

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

niharika_kumar

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From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: integration

one more question.
integrate the following:-

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Bob

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Re: integration

Haven't tried this yet but it may work.

Change cos^8 into sines.  Then you have lots of powers of sine and one cosine (as the derivative of sine) so it is maybe directly integrable then using what I said earlier.  Got to make an important phone call so I'll give it a try properly later.

EDIT:  just tried it and this does work.  You get integral of cos/sin and a string of odd pwers of sin multiplied by cos.

eg.

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

niharika_kumar

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From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: integration

hmmm, thanks.

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niharika_kumar

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From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: integration

but the answer given is:-

where C is the integral constant.
and unfortunately I am not able to reach this.

help.

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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: integration

One IBP and a reduction formula might produce that answer. But since you have not given the conditions under which the problem must be solved I have not worked on it.

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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.

Bob

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Re: integration

hi Niharika

Oh joy, that answer is what I got.  Like this.

Notice that cos(x) is the derivative of sin(x).  So try to get an expression where each term is a power of sine multiplied by a single cos.

So you split into separate terms, divide each by the sin(x) and then use the function and its derivative idea to integrate the terms.  I did one for you back a few posts.

Can you finish it from here ?

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

niharika_kumar

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From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: integration

yes i got it.
thanks again.

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Agnishom

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From: Riemann Sphere

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Re: integration

How do I integrate

with respect to x?

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anonimnystefy

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From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: integration

That's just ln|x-k|.

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Agnishom

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From: Riemann Sphere

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Re: integration

I know but how do I do it?

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

anonimnystefy

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From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: integration

By substitution.

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“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.

Agnishom

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From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

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Re: integration

Show it, please

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: integration

Have you tried taking u=x-k?

I am not home at the moment. I'm on my phone.

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“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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: integration

Hi Agnoshom

Back now. Were you able to do it?

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“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.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: integration

No, I am bad at integration

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: integration

Hm, I'll show you in a few minutes.

Last edited by anonimnystefy (2014-06-17 12:04:51)

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“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.