X=acos^3t,y=asin^3t 所围成的平面图形的面积

来源：学生作业学帮网编辑：学帮网时间：2024/05/05 02:29:27

x=acos^3t,y=asin^3t是星形线,它的面积为
∫ydx=4*∫asin^3t(acos^3t)'dt,t:π/2→0
=-3*a^2∫sin^4t*cos^2tdt
=-3a^2∫(sin^4t-sin^6t)dt
=3/8*πa^2

S = |2∫ydx| (t=0到t=π) = |2∫asin^3t * a*3cos^2t*(-sint)dt| = 6aa∫sin^4tcos^2tdt
= 6aa/5 ∫sin^6tdt
=3aa/20π
只能输100字，没办法了

参数方程确定的函数的求导。 dy/dx=3asin^2tcost/[-3acos^2t sint]=-tanx d^2y/dx^2=-sec^2t/[-3acos^2t sint]=1/[3acos^4t sint].

y=[a^(2/3) - x^(2/3)]^(3/2) （设a>0)
S=4 定积分(0,a) ydx, 令x=a^(2/3) cos^2 t
S=4 定积分 -2/5 a^(2/3) sin^5 t
=8/5 a^(2/3)(1-a^(2/3) )^5

x=acos^3 t y=asin^3 t x=acos^3t,y=asin^3t,求dy/dx 用格林公式求星型线 x=acos^3t,y=asin^3t的面积, x=acos^3t,其中a不等于0求二阶导数?y=asin^3t X=acos^3t,y=asin^3t 所围成的平面图形的面积请问X=acos^3t,y=asin^3t 如何知道他是围成什么样的图形呢星形线x=acos^3t,y=asin^3t所围成的面积 X=acos^3t,y=asin^3t 所围成的平面图形的弧长星形线x=acos^3t,y=asin^3t(a>0)所围成的面积帮忙看看这道题怎么搞,求曲线x=acos^3(t),y=asin^3(t)在t=t0处的曲率.^3代表3次方 x=acos^3t y=asin^3t 在t=π/6时,求相应点切线方程和法线方程 x=acos³x y=asin³t 求d²y/dx² x=acos³x y=asin³t 求d²y/dx² 星行曲线,x=acos^3t,y=asin^3t,求曲线所围成的面积?不然,我看不懂. x=acos三次方t y=asin三次方t a为常数 t为角度求导微分题,求曲线y=acos't,x=asin't在点（x(t),y(t)）处的切线L(t)的方程求由x=acos^2t,y=asin^2t所围成的图形的面积如何x(t)=cos(t)+asin(t) y(t)=sin(t)+bcos(t) expressing x(t) in the form Acos(t-α)和y(t)=Bsin(t-β) ?、急在线等

X=acos^3t,y=asin^3t 所 围成的平面图形的面积