求由曲线x=t-t^3,y=1-t^4所围图形的面积最好能有图

Question

求由曲线x=t-t^3,y=1-t^4所围图形的面积 最好能有图

Answer 1

先求交点：t-t^3=1-t^4
t1=1 t2=-1
dA=(1/2)*∮(xdy-ydx)=0.5∮[（t-t^3)（-4t^3)-(1-t^4)((1-3t^2)]dt
=0.5∮[（t-t^3)（-4t^3)-(1-t^4)((1-3t^2)]dt
=0.5∮[（-t^4+2t^2-1)]dt
=0.5*2∫（0,1）(1-2t^2+t^4)dt=(t-2t^3/3+t^5/5)|(0,1)=8/15