A) The region R is bounded by the curves y=2x, y= 7-x^2 and the y-axis, and its mass density id d(x,y) = x.y. To find the center of gravity of the region compute,

integral integral R d(x,y) d A = integral ( c to d) integral ( p(x) to q(x) ) d(x,y) dy.dx, integral (c to d) integral (p(x) to q(x)) xd(x,y) dy.dx, and integral ( c to d) integral ( p(x) to q(x) ) y d(x,y) dy.dx where,

c= ….

d= ….

p(x) = ….

q(x) = ……

integral (c to d) integral (p(x) to q(x) ) dy.dx = ….

integral ( c to d) integral ( p(x) to q(x) ) x dy.dx = ……

integral ( c to d) integral ( p(x) to q(x) ) y dy.__?__dx = ….

and finally the center of gravity is

x( bar) = …

y( bar) = ….