1,求曲线y=x²与x=1所围平面图形面积及其绕y轴旋转所得旋转体面积 2,xy=e^x+y,求dy

对于y轴,面积A由x=√y及x=1围成
A=∫(0到1) (1-√y) dy
(y-2/3*y^3/2)(0到1)
=1-2/3
=1/3
绕y轴旋转所得的体积
Vy=π∫(0到1) dy-π∫(0到1) (√y)^2 dy
=π(y)|(0到1)-π(y^2/2)|(0到1)
=π-π/2
=π/2
xy=e^(x+y)
y+x*dy/dx=e^(x+y)*(1+dy/dx)
y+x*dy/dx=e^(x+y)+dy/dx*e^(x+y)
dy/dx[x-e^(x+y)=e^(x+y)-y
dy/dx=[e^(x+y)-y]/[x-e^(x+y)]
∴dy=[e^(x+y)-y]/[x-e^(x+y)] dx