Question: A metal plate, with constant density 2 gm/cm2, has a shape bounded by the two curves y = x2 and y = √x, with 0 ≤ x ≤ 1, and x, y in cm.
(a) Find the total mass of the plate.
(b) Because of the symmetry of the plate about the line y = x, we have = . Sketch the plate and decide, on the basis of the shape, whether x¯ is less than or greater than 1/2.
(c) Find x¯ and y¯.