How Do You Calculate the Area Bounded by a Polar Curve?

[will_lansing]

[SOLVED] Area of Polar Coordinates

Homework Statement

Find the area of the region bounded by r=6-4sin$$\Theta$$

Homework Equations

A=(1/2)$$\int$$ r$$^{2}$$ d$$\Theta$$

The Attempt at a Solution

I'm not sure what the bounds are but I thought they were 0 to 2pi. Am I wrong if so how then do you go about finding the bounds?
A=(1/2)$$\int$$ [36-48sin$$\Theta$$+16sin^2$$\Theta$$ d$$\Theta$$
A=(1/2)[36$$\Theta$$-48cos$$\Theta$$+8$$\Theta$$-4sin2$$\Theta$$]

and i got the answer to be 63.5 where did i go wrong?

 

[arildno]

How do get $$44\pi=63.5$$?

 

[will_lansing]

I'm not sure what i did. I think i typed in the wrong thing in my calculator or something. but i just plugged 2pi and 0 in for theta, but i still got the wrong answer. What am i suppose to do.

 

[arildno]

Do it by hand, then, and see if you get 44*pi.

One possible reason why your calc gave you something else than that might be that your calculator is measuring angles in degrees instead of radians.

 

[will_lansing]

yeah you're right i forgot to change back to radians, i feel so stupid now. well thanks, maybe i should just do by hand and not put so much trust in the calculator.