A(a,a^2)
y'=2x
所以切线斜率k=2a
所以y-a^2=2a(x-a)=2ax-2a^2
y=2ax-a^2
和x轴交点(a/2,0)
y=x^2在切线上方
所以S=∫x^2dx[积分限是0到a/2]+∫[x^2-(2ax-a^2)]dx[积分限是a/2到a]
=x^3/3(0到a/2)+(x^3/3-ax^2+a^2x)(a/2到a)
=a^3/16+(a^3/3-a^3+a^3-a^3/16+a^3/4-a^3/2)
=a^3/3+a^3/4-a^3/2
=a^3/12=1/12
a=1
A(1,1)