Find the moments about the x-axis M x
​
and the y-axis M y
​
and the center of mass ( x
ˉ
, y
ˉ
​
) of the region R. Assume density is constant throughout the region. (a) The region B is bounded by y=2x,y=x 3
−2x 2
−x,0⩽x⩽3. (b) The region B is a trapezoid with vertices (2,1),(5,1),(6,3), and (2,3). 12) Solve. (a) dx
dy
​
= y
2x+1
​
​
,y(0)=−2 (b) dx
dy
​
=6x 2
y−9x 2
+2y−3,y(0)=− 2
1
​
(c) dx
dy
​
= (x−1) 2
(y−2) 2
​