' File XIX_db8
' Given the  curve, r =2cos(x) + 1,  find the area of the smaller loop.
pi = 3.14159  :  p2 = 2pi

F{x,r} = r  :  C{x} = 0  :  D{x} =2cos[x] + 1 :  a =2 pi/3  :  b = 4pi/3

n = 10 : m = n   ' Panels.
ar = dblint[F, C, D, {a, b, n, m, y}]

' ************ Optional Plot ************
R{t} = 2cos[t] + 1
X{t} = R{t}*cos[t]
Y{t} = R{t}*sin[t]
P<t> = <X, Y, 0>
Plot[P, {t, 0, p2, 50}]

'@Area = @ar, square units.!



