7. Find the center of mass of the lamina bounded above by f (x) = -x + 4 and below by g(x) = x over [0,2] on the x-axis. Assume p = 1.5. Make sure to draw the region on the axis provided and label your point for the center of mass. 1) m = PS ( ( - X - 4 ) - ( * ) ) dx = PS ( * + 4 ) - x ) d * - F ( 2 4 x )2x = 1.5 ( x3 - 4 x " ) :- 7.999 X 2 really ... 2 ) Mx 1.5 ( [ ( - X + 4 ) ] 2 [ ( x ) ] 2 dx 2 271 directin to 1:25 (2( - x +4 ) - * 4 ) ex : (2 ( - x + 4 ) 2 19 - - x ( x + 4 x - x + 4 ) or 2 ( - X + 4 ) 1 2 ( 2 ( 24 # ) 2 23 ) = - 2 x 2 - 4 x - 4x + lc w-sub ? yes .. but how ? 3) my = PS * ( ( - * +4 ) - ( x ) ) dx - 3.99 9 - 6 x My = 3.999 7.999 y = My = Jaa ( -. 4999) 2500 )4. Find the volume of the shape generated by the region bounded above by fox) = -x + 1, below by y = 1 from [-2,0] on the x-axis about the line x = 2. You may use any method you wish (Cylindrical Shells, Washer, or Disk Method.) To receive full credit, make sure to show all calculus- -0.5 based steps, justification for your limits of integration, all the arithmetic computations, and provide a sketch shopper. of the region, the shape generated, and a representative slice/shell for your calculations. 0 -Not =) T ( - x + 1 ) 2 dy IT S (-x + 1) 3 TT ( - * + 1 ) 5 - 8 -2 3 check ustes. ( - 333 ) - 9 = - 9.3 3 1