Find the area bounded by the curve given by the equation:
How do you transform the equation to the integral?
Solve for y:
We need to keep the "+" solution else y isn't real. So:
Thus
The area you are after will be between the "+" and "-" curves, and you know by symmetry they cross on the x-axis so you should be able to find these fairly easily. The integral you will be doing will be of the form:
which isn't going to be at all pretty. You'll likely have to do a numerical estimate. (Unless Krizalid or someone else pulls a trick out of their hat.)
-Dan
If this is the Leminscate of Bernoulli.
Express this curve in polar coordinates for simplification.
This is Mine 69th Post!!!
Hellow, kezman!
I would convert to polar coordinates . . .Find the area bounded by the curve given by the equation:
. .
Conversions: .
Then we have: .
. . which simplifies to: .
This looks like a large Infinite-sign:
. . It is symmetric to both the "x-axis" and the "y-axis".
We can integrate from to and multiply by 4.
. .
Got it?