Question

求由曲线y=x的平方2,x=y的平方2所围成的平面图形的面积S,以及该平面图形绕x轴旋转转一周所得旋转体体积V

Answer 1

S=∫(0,1)[x(1/2)]dx-∫(0,1)[x^2]dx

=[2/3(x^(3/2))-1/3(x^3)](0,1)

=2/3-1/3

=1/3

V=π∫(0,1)[x]dx-π∫(0,1)[x^4]dx

=π[1/2(x^2)-1/5(x^5)](0,1)

=3π/10