Example//Calculate second moment of inertia about y-axis for area enclosed by y=x², y=x+2. Solution // ly = ff x² dA J1=y2 x² = x+2 x2 x 2 = 0 (x-2)(x + 1) = 0 X=2 or x=-1 2 x+2 = [] x²dy dx = [][]*~²dy dx = = SS 2 2 = r² = -1 x+2 -1 x2 (x²y)| dx x² x²(x+2x2)dx = 365 unit of length 2x3 x4 + 4 3 - x5 2 5 Example// Find the centroid enclosed function Y=6x-x². y=x Solution / My Mx X = Y = A A У1=92 6x-x² = x x²-6x+x=0 x2 – 5x = 0 X (x-5)=0 X=0 or x=5 A=ſſ dy dx = √5 √6x¯x² dy dx = √5 (y)| 6x-x² dx = x²x) dx = 125/6 Mx=ff ydA = ff y dy dx 5 1x = √5 (6x- Mx=√ √6x-x² ydy dx = So³ (²) | 6x-x² dx = 5 (6x-x²)2 (x)²) dx = 104.16 2 Also My=625/12 X = My A = Mx Y = = 625 12 125 = 2.5 104.16 A 125/6 = 5 x 2