1) You may find the center of mass (centroid) of a lamina by the following integrals A = \\" f ( x ) dx X xf (x) dx A a and y : I' ( f ( x ) )' d x center of Mass Find the exact center of mass of a lamina ( thin flat uniform dense plate) bounded by f (x ) = cos x ; y = 0; 05x5- 2 the approximated answer is (0.5708, 0.3927)2) To calculate the defection of curved beams one may need to evaluate the following integral 1 1 dx I0 dy 2 Using trigonometric substitutions evaluate 1 + [J this integral for y = x2