不定积分x^2dx⼀((a^2-x^2)^(1⼀2))

2025-03-24 02:13:41
推荐回答(2个)
回答1:

0

回答2:

x=a*sint,t=arcsin(x/a),dx=a*cost*dt
不定积分x^2dx/((a^2-x^2)^(1/2))
=Sa^2*(sint)^2 *a*cost *dt /a*cost
=Sa^2 *(sint)^2 *dt
=a^2 /2 *S(1-cos2t)*dt
=a^2 /2 *t-a^2 /4 *sin2t+c
=a^2 /2 *arcsin(x/a)-1/2*x*根号(a^2-x^2)+c