z=(1-r^2)^0.5
体积=4*∬(1-r^2)^0.5*rdrdθ=2pi/3
2*∬(Dxy)(1+(∂z/∂x)^2+(∂z/∂y)^2)^0.5dxdy=∬1/(1-r^2)^0.5*rdrdθ=pi/3
y=(x-x^2)^0.5
弧长高度f(x,y(x))=(1-x^2-y^2)^0.5=(1-x^2-(x-x^2))^0.5=(1-x)^0.5
y'=0.5*(1-2x)/(x-x^2)^0.5
4*对弧长的曲线积分∫(L)f(x,y)ds=4*∫(a到b)f(x,y(x))(1+y'^2)^0.5dx
=4*∫(0到1)(1-x)^0.5*(1+(0.5*(1-2x)/(x-x^2)^0.5)^2)^0.5dx=4
表面积=pi/3+4