用参数方程代入x=cost,y=sint代入:
fL(2x^2 -xy+ 3y^2)ds
=fL( y^2-xy)ds
=∫(0, 2π)(sin^2t-sintcost)dt
=∫(0, 2π)sin^2tdt
=∫(0, 2π)(1-cos2t)/2dt
=π
用参数方程代入x=cost,y=sint代入:
fL(2x^2 -xy+ 3y^2)ds
=fL( y^2-xy)ds
=∫(0, 2π)(sin^2t-sintcost)dt
=∫(0, 2π)sin^2tdt
=∫(0, 2π)(1-cos2t)/2dt
=π