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ilovealgebra

Member

Registered: 2006-10-02

Posts: 40

Integration in polar coordinates

Hi I am required to find the following iterated integral by converting to polar coordinates

This is what I've done so far...

Now what do I do?? Can you simplify the integral to...

Or is there some other neat way of doing it?

Cheers guys!!

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"...nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called into question (much less condemned) upon the testimony of biblical passages."
-Galileo Galilei

Bob

Administrator

Registered: 2010-06-20

Posts: 10,375

Re: Integration in polar coordinates

hi ilovealgebra

I've been hoping someone else would pick this up and then I'd learn something.  But no one has so I'll throw in my small contribution just to show you're not being totally forgotten.

(i) 

I don't think this is ever going to simplify to

because

=

=

=

Why did you want this anyway?

(ii)  I need help following where your new limits came from.  Perhaps if you explain to me it will help you clarify what you have done so far.  I often find that helps.

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,375

Re: Integration in polar coordinates

Just had a brainwave!

Make use of

so

=

=

so the integral is

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: Integration in polar coordinates

Hi all;

For one thing:

And:

So 2) is not a simplifcation of 1).

That answer is correct as long as you do not forget to divide it by 3.

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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.

ilovealgebra

Member

Registered: 2006-10-02

Posts: 40

Re: Integration in polar coordinates

Oh my God facepalm!!! For some reason I thought

Ahh cra.p sorry guys epic fail there!!

Sorry to waste your time guys! argh!

---

"...nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called into question (much less condemned) upon the testimony of biblical passages."
-Galileo Galilei

Bob

Administrator

Registered: 2010-06-20

Posts: 10,375

Re: Integration in polar coordinates

hi ilovealgebra,

You're welcome.  No problem about not spotting an error.  I always read through my posts but still read over and miss silly errors.  That's why it's useful to exchange ideas.

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