Planimeter Sweeping Out Area
Signed Area Swept Out by Infinitesimal Motions
Translations
dA = l d
s
Rotations
dA =
-
1
/
2
l
l
2
d
q
Total:
dA = l d
s -
1
/
2
l
l
2
d
q
Integrate to get
signed area swept out
A = l
s -
1
/
2
l
l
2
Dq
Combine with
Moving Segment Theorem
A
R
-
A
L
= l
s -
1
/
2
l
l
2
Dq
Measuring a Region
