The region R is bounded by two curves y=x^2 and y = sqrt(x). They intersect at two points x=0, y=0 , and x=1, y = 1. Mass is equal to the integral of p(x,y) dxdy = int kydxdy. limits of integration by x are variable:
x = y^2 for lower limit and x = sqrt(y) for upper limit (since 0<y<1, y^2 < sqrt(y)).. Integration by x gives us
mass = int ky(sqrt(y) - y^2)dy = 3k/20 = 0.15k.
The function p(x,y) represents the surface density, and these calculations are true for infinitely thin plate only.