We write and which simplifies into ,but why is differential area now?

and (Wondering)

Also on a sidenote, if I rewrite as .

(I know that .)

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- Nov 7th 2010, 01:50 PMcourteousChange to polar coordinates

We write and which simplifies into ,**but why is differential area now**?

and (Wondering)

Also on a sidenote, if I rewrite as .

(I know that .) - Nov 7th 2010, 02:21 PMTheEmptySet
Here is why

Polar coordinate system - Wikipedia, the free encyclopedia

You can also draw a picture of a polar rectangle and calculate is area directly this is a very informal justification

Attachment 19622

Finally you need to calculate the new limits of integration in Polar coordinates.

Sketch the first quadrant and now decided what values and need to vary between to sweep out the first quadrant.

I hope this helps - Nov 7th 2010, 10:58 PMcourteous
I am not questioning the correctness of . So, you have to consider the Jacobian determinant (of the coordinate conversion formula)? And if you just differentiate as usual (the way I did it) it is just wrong?

- Nov 7th 2010, 11:03 PMProve It
- Nov 7th 2010, 11:36 PMcourteous
I meant differentiate and . What is wrong with my algebraic "reasoning" above?

- Nov 7th 2010, 11:54 PMmr fantastic
Read pp6-7 here: http://mathstat.carleton.ca/~amingar...oordinates.pdf

Most textbooks that cover vector calculus have a derivation of the jacobian. I suggest you visit your library. - Nov 8th 2010, 12:54 PMcourteous
I've just been to library today. (Nod)

Quote:

The lyf so short, the craft so longe to lerne.

*pdf*!