Finding the area enclosed by r=3sin theta

[grog]

Homework Statement

Find the area enclosed inside r=3 sin (theta)

Homework Equations

integral?

The Attempt at a Solution

basically, I took $$\int3sin\Theta$$ from 0 to 2pi, then pulled the 3 out to get

$$3\int sin\Theta$$ from 0 to 2pi and then

$$3[-cos(\Theta)]$$ evaluated from 0 to 2pi.

that seems too easy. what am I missing?

 

[Dick]

Who said everything has to be super hard? But if you work that out, you'll get 0 for the area. Is that right? It might help to draw a picture. And, hey, area in polar coordinates isn't the integral of r dtheta, is it? Would you look up the right formula for area?

 

[grog]

ah. that's what it was. I forgot about the formula for area. : (

Thanks!

 

[HallsofIvy]

Who said everything has to be super hard? But if you work that out, you'll get 0 for the area. Is that right? It might help to draw a picture. And, hey, area in polar coordinates isn't the integral of r dtheta, is it?

Well, actually, Dick, area in polar coordinates is r dtheta! You didn't say quite what you meant to, did you?

Would you look up the right formula for area?

 

[Dick]

Well, actually, Dick, area in polar coordinates is r dtheta! You didn't say quite what you meant to, did you?

Are you SURE?

 

[Dick]

The integral of r*dtheta*dr is the area. Not the integral of r*dtheta. I missed it at my first reading as well.