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sqrt b²x-a²
x= a/b sec theta
use sec² = tan² + 1
sqrt a² - b²x²
a/b sin theta
use 1-sin² theta = cos² theta
sqrt a² + b² x
x = a/b tan theta
looks like tan² +1 = sec² theta
integral of sec²x =
tan x
sec x tan x integral
sec x
center of mass
a b x px dx / a b px
length of curve
a to b sqrt 1 + f’(x)²