Converting cartesian to polar coordinates in multiple integrals

[robertjford80]

Homework Statement

Do you see how y gets converted to csc? I don't get that. I would y would be converted to sin in polar coordinates.

 

[Karamata]

<deleted>

 

[robertjford80]

thanks, I got it.

 

[robertjford80]

I need to see what Karmata wrote again, if anyone knows I would appreciate it.

 

[robertjford80]

still needing

 

[Karamata]

Hi robertjford80!

I deleted my post because there was error in him (oh, bad English)

But, look at picture.

They said \int_0^6 \int_0^y x \mbox{d}x\mbox{d}y, that is yellow region (x from 0 (parallel y-axes) to x=y, y from 0 to 6). r is moving from r=0 to y=6, so, y= 6= r \sin \theta \Rightarrow r = \dfrac{6}{\sin \theta} = 6 \csc \theta

 

[robertjford80]

ok, thanks, I got it. this so far has been one of the most difficult concepts in calculus to understand but I'm slowly getting it.