Question

Trying (mightily) to find an integral using cylindrical coordinates. Problem and work attached.

Answer 1

\[\int\limits _6^{12}\int\limits _0^{\sqrt{x^2+y^2}}\frac{1}{\sqrt{x^2+y^2}}dydx\]

Answer 2

hint: \[\ \large \frac{1}{\sqrt{x^2+y^2}} \ ;\ a= x \ , \ u= y\]\[\ \large \frac{1}{a} \tan^{-1}\left( \frac{u}{a}\right)\]

Answer 3

But looking at the problem now I don't think it'll help much :(

Answer 4

Yeah. I think I'm getting lost on the conversion to cylindrical. The function ends up being \[\frac{1}{\sqrt{r^2}}\], but I'm not sure what to do for the boundaries.

Answer 5

@dan815 a little assistance? :)

Answer 6

what program did you use to draw that ?

Answer 7

Mathematica for the typed piece, Photoshop for the handwriting.

Answer 8

And I'm a lot better at the latter. :)

Answer 9

top half

Answer 10

wait what the hek.. ur bound doesnt make sense

Answer 11

oh so its y=0 to y=sqrt(x^2_y^2)>

Answer 12

?

Answer 13

is ur bound wrong or something?

Answer 14

That would be the whole upper half of the circle wouldnt it be?

Answer 15

you used a different bound in your picture compared to the main bound

Answer 16

tell me ur question as it is, or im leaving you!

Answer 17

Ooops, my bad. That should read: \[\sqrt{12 x-x^2}\] for the top limit.

Answer 18

ok =]

Answer 19

Damn.

Answer 20

I got a little sloppy with the copy and paste.

Answer 21

Wait, can you rewrite the integral? D:

Answer 22

I'm still a little confused.

Answer 23

okay lets look at the region again, i believe its justa circle displaced on some axis