Hi, I am having trouble with this problem. Any help would be appreciated.
Calculate the area of the region bounded by the curve
(x^2+y^2-x)^2=x^2+y^2 and the circle x^2+y^2=sqrt(3) y
Thanks
Hello, 0pokerman0!
Convert to polar coordinates . . .Calculate the area of the region bounded by
the curve: . .and the circle: .
Take the square root: .
Divide by . . . a cardoid.
. . a circle with center on the "y-axis", through the origin, with diameter
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Now try it . . .
Hello again, 0pokerman0!
We see that the two curves intersect at the origin.
Find the other intersection:
. .
Divide by 2: .
Since:
. . we have: .
Then: .
This requires two integrals . . .
. . the area in the circle from
. . the area in the cardioid from