显式方程y=f(x (axb 参数方程x=x(t,y=y(t (t 极坐标方程r=r(θ (
根式的形式
平面图形的面积 平面曲线的弧长公式
b旋转面的面积 曲率
Sf(xg(xdx
absba1f'(xdx
2F2f(x1f'2(xdxaK若为直线方程,则Fl(yAyBF2y(tx'2(ty'2(tdtddsy''21y'32
Sydxy(tx'(tdt
sx'2(ty'2(tdt
若以弧长为参数,则F2y(sds0l
x'(ty''(tx''(ty'(td K3ds222x'(ty'(tS122r(r(d212
baSr2(r1(rdrsr2(r'2(d
F2r(sinr2(r'2(d
所作替换
xasint,xatant,原根式变为
ax ax