Finding centroid

Question

A quarter with the center at the origin and radius of 1 unit is out from a square with side of 1 unit. the square has its lower left corner at the origin. Determine the centroid of the remaining area.

Answer 1

area is 1 *1 - pi(1^2) = 1 - pi

f(x) = 1

g(x) = sqrt(1-x^2)

f(x)-g(x) = 1 - sqrt(x)

x( 1 - sqrt(x)) = x - x*Sqrt(x) = x - x^(3/2)

X = integral[ x - x^(3/2) ] , x=0..1

= (1/2)x^2 - (2/5)x^(5/2), x = 0..1

= (1/2-2/5) = 1/10

(1/10)(1/(1-pi)

Y = integral ( 1 - x), x=0..1

1 - (1/2)x^2

= (1/2) - 1 = -1/2

(-1/2)(1/(1-pi))