I have no idea what this solution to this centroid problem is talking about. Can
ID: 2865103 • Letter: I
Question
I have no idea what this solution to this centroid problem is talking about. Can someone please explain
y = (b - a/h)x + a dA = y dx A = integral dA = integral^h_0 [(b - a/h)]dx = [b - a/h x^2/2 + ax]^h_0 = h/2(a + b) integral x_c dA = integral^h_0 [(b - a/h)x^2 + ax] dx = [b - a/h x^3/3 + ax^2/2]^h_0 = h^2(b/3 + a/b) integral y_c dA = integral y/2 y dx = 1/2 integral^h_0 y^2 dx = 1/2 integral^h_0 [(b - a/h)^2 x^2 + 2(b - a/h)ax + a^2] dx = 1/2 [(b - a/h)^2 x^3/3 + 2(b - a/h) a x^2/2 + a^2 x]^h_0 = h/6 [a^2 + ab + b^2] x- = integral x_c dA/A = h^2(b/3 + a/6)/h/2 (a + b) = h(a + 2b)/3 (a + b) y- = integral y_c dA/A = h/6(a^2 + ab + b^2)/h/2(a + b) = (a^2 + ab + b^2)/3(a + b)Explanation / Answer
The solution gives the position of centroid of the given figure