Let R be the planar region between the curves y^2 + (x-1)^2 = 4 and y^2 = 3(x-1) which contains the point (0, 0).
1.) Calculate the total area of R.
2.) Determine the total length of the boundary of R.

Question

Let R be the planar region between the curves y^2 + (x-1)^2 = 4 and y^2 = 3(x-1) which contains the point (0, 0).
1.) Calculate the total area of ​​R.
2.) Determine the total length of the boundary of R.

amistre64 · Answer

we got an interval to work with yet?  or is this going to be one of those multivariate things

amistre64 · Answer

y^2 + (x-1)^2 = 4

seems to be a circle centered at 1,0 of radius 2

y^2 = 3(x-1)
1/3 y^2 +1 = x

parabola on its side with vertex at 1,0 i think

anonymous · Answer

i think y varies from (-sqrt(4-(x-1)^2) to (+sqrt(4+(x-1)^2))
and x to -1 to 1

amistre64 · Answer

|dw:1353646297340:dw|

amistre64 · Answer

think my parabola is a little off

anonymous · Answer

amistre is my upper and lower limits right?

amistre64 · Answer

depends on which way youre integrating

anonymous · Answer

that + sqrt(4-(x-1)^2)

amistre64 · Answer

|dw:1353646558266:dw|

i was thinking of doing shells rotated about the x axis