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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.
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) = ....
