Question

Where do this mysterious R come from? (Look at Attachment)

At the end, an r has SOMEHOW gotten inside the dr; which I do not understand. Where did it come from?!

Answer 1

Q: Where do the R come from

Answer 2

http://tutorial.math.lamar.edu/Classes/CalcIII/TICylindricalCoords.aspx

Answer 3

I hope this helps

Answer 4

I am aware of cylindrical coordinates; my problems are not the cylindrical coordinates. However, my question where they just pulled an extra R and put it in the formula.

Answer 5

If you look at the web I posted, there is an R when you transform dxdydz to drdthetadz,

Answer 6

since d(x,y,z) = 8, and we put it into the formula; there should not be an extra r though

Answer 7

Ill check it out further

Answer 8

This is because dxdy=rdrdtheta

Answer 9

ohh..

Answer 10

remember the area of circle is pi*r^2, right. Now pi turns into theta because the angle is not set to pi. And take infimitesimal of both r and theta, you end up with rdrdtheta

Answer 11

Thanks :)

Answer 12

Its a result of the Jacobian