Answered>Order 2599
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) =xy. To find the center of gravity of the region you would compute
integral integral R d(x,y) dA = integral ( c to d) integral ( p(x) to q(x) ) d(x,y)dydx, integral (c to d) integral (p(x) to q(x) x d(x,y) dydx, and integral ( c to d) integral ( p(x) to q(x) ) y d(x,y) dydx where,
c= ….
d= ….
p(x) = ….
q(x) = ……
integral (c to d) integral (p(x) to q(x) ) dydx = ….
integral ( c to d) integral ( p(x) to q(x) ) x dydx = ……
integral ( c to d) integral ( p(x) to q(x) ) y dydx = ….
and finally the center of gravity is
x( bar) = …
y( bar) = ….