Math Is Fun Forum

gairceilatan

Member

Registered: 2007-05-22

Posts: 7

Integration

Hey,

Can someone help me with this type of question?

∫cos(x²)dx

I know how to diffrentiate it but I have no idea how to integrate it and I can't figure it out by working back the way .

Many thanks

Zhylliolom

Real Member

Registered: 2005-09-05

Posts: 412

Re: Integration

Is this a homework assignment for a class? If so, what class? Are there any limits of integration for this integral? This integral is known as a Fresnel integral. If the integration is done from 0 to ∞, it's not very hard to calculate the integral if you know what the gamma function is. There isn't really much to do with this if it is an indefinite integral though.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Integration

I managed to turn it into

, where u = x², but that probably just makes it harder.

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Why did the vector cross the road?
It wanted to be normal.

gairceilatan

Member

Registered: 2007-05-22

Posts: 7

Re: Integration

Hi,

I'm doing first year maths at uni and it was on a change of variable worksheet and the whole question was

∫x cos(x²) dx

I have no notes with an example like this and had no idea where to start.

Thanks for your help mathsyperson and Zhylliolom although i'm still not really sure on this at all.  I may have turned it into something harder by not putting the whole question down, however I would be grateful for any help you can give me. 

thank you

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Integration

that makes it alot easier lol

wait.. your in uni, im still doing gcse's, how does that work (well im actually doing my alevel early, just taken my last module on monday)

Last edited by luca-deltodesco (2007-05-22 08:06:51)

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Integration

Yes, in the first year of Uni you tend to recap some of the stuff you do in A-Level. Unis don't trust that you've learnt anything so they teach it to you again.

Having said that, if I remember correctly that would be quite advanced stuff for A-Level. I think it might be Further Maths, although I'm not sure. What modules are you sitting early? You might have self-learned this bit.

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Why did the vector cross the road?
It wanted to be normal.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Integration

Uh oh, see why the whole question is so important in maths?

Actually the orginal integral is unintegrable, I mean cannot be expressed by simple combinations of functions , +-*/sincostanlog.

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X'(y-Xβ)=0

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Integration

Yes, in the first year of Uni you tend to recap some of the stuff you do in A-Level. Unis don't trust that you've learnt anything so they teach it to you again.

Having said that, if I remember correctly that would be quite advanced stuff for A-Level. I think it might be Further Maths, although I'm not sure. What modules are you sitting early? You might have self-learned this bit.

i havnt done any further maths formally, although ive already leant some complex algebra and some linear math and things to do with finding critical points on surfaces etc.

ive done core 1-4, stats 1 (all A's) took my Mech 1 exam 2 days ago, and my Mech 2 exam is in a couple of weeks, this isnt further maths though: a quick look into my core3+4 textbook, this is a qestion in the optional section after all the substitution stuff, under the title 'choosing a suitable substitution'

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Integration

Ah, OK then. In that case, Further Maths must go on to do more general differential equations.

So far, it's always been dy/dx = f(x), where f(x) is the thing you're integrating, but in Further Maths that gets mixed up a bit. And then after that you do 2nd order differential equations, which are somehow easier than the first order ones.

Great fun.

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Why did the vector cross the road?
It wanted to be normal.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Integration

actually, towards the end of core 4 you start getting more of the type of question your talking about there under implicit equations

for example:

and then subsequently working backwards:

which is where i pulled in the use of partial derivitaves to help with more complex equations involving heavy use of product/chain rule etc, using the rule that i discovered myself:

for example:

or:

not as useful in this case, but you can see it could be useful

Last edited by luca-deltodesco (2007-05-23 01:43:17)

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gairceilatan

Member

Registered: 2007-05-22

Posts: 7

Re: Integration

Hi there,

Thank you everyone for your help I am sorry about not putting the whole question I like to work things out for myself, helps me remember what to do, so I thought if I could integrate cos(x²) I would have been able to solve the equation on my own.  I see now I just make the question much harder.

I live in Scotland and I only sat higher maths before going to uni which does not go as far as A-level does so this is all new to me.  Should have done the advanced higher

Thanks again for all your help

Last edited by gairceilatan (2007-05-23 03:52:49)