Math Is Fun Forum

ilovealgebra

Member

Registered: 2006-10-02

Posts: 40

Double Integral in Polar Coords

Use a double integral in polar coordinates to find the area of the region enclosed by the rose

My working is as follows:

     

     

     

     

However I don't think this is correct since it seems to be the same area as the circle with r=1. Can someone please tell me where I've gone wrong? (Also Anton says It's wrong )

Cheers for the help!

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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: Double Integral in Polar Coords

Hi ilovealgebra

Where did the 2theta come from in the penultimate line ?

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Double Integral in Polar Coords

Hi;

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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: Double Integral in Polar Coords

Ahh well when i differentiate

I end up getting

So yeah, I forgot to divide by the coefficient of theta, which was 2 in this case.

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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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Double Integral in Polar Coords

Everything check out now? Where are you in the book?

---

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: Double Integral in Polar Coords

Yeah all good, just working my way through chapter 15.3 then will be moving onto 15.5 & 15.7

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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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Double Integral in Polar Coords

Hi ilovealgebra;

Good luck and study hard. Do not forget to take GG with you!

---

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: Double Integral in Polar Coords

Haha I'll try my best=)

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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